Put it this way, do you think you could keep up the discipline & schedule necessary for competitive sports while working 2 full time jobs?  

Is it possible to do both?  I'm sure it is.  But one or both would suffer, not to mention the whole "sleep" thing.  Worth considering for a minute, then realizing each is a full-time job.

If you treat it like an actual job with defined hours & not the way a large chunk of you're studio cohort will, its possible. Architecture school will expand to fill whatever time you allow it to. There will be some kids who practically live there & there will be others that you see come in, put their headphones on & crank something out in 6 hour's & leave. My undergraduate class had an athlete, he was that way.

The trouble comes with the travel schedule.

You specified M.Arch, do you already have a bachelors' degree in architecture? Part of the struggle is learning how long it takes you to make certain kinds of output, whether its a model, a drawing, etc. Early on in your education the outputs are pretty prescribed, where as in grad school (at least my case) we were allowed to provide "whatever supporting materials best conveyed our ideas". Which for me meant that I stopped making things that the time / value ratio wasn't in my favor.

Well Andrew Luck did a Bachelor's in Arch Design while being a top QB. Granted, it was a college degree and Stanford doesn't have a design school proper. But I heard that he was very focused and efficient with his time - style and flash were secondary to efficient space planning and execution as far as design assignments go. He got the job done in studio and that was it.

I know a lot of D3 Lacrosse Coaches/Programs did not allow their athletes to play lacrosse as Architecture Majors. Maybe that's changed, but I wouldn't be surprised if it hasn't. What sport(s)? 

Like RJ87 said the biggest issue with be travel times/commitments. Especially if you're expected to produce analog (physical models, hand drawings, etc) deliverables. I think your best bet would be finding a smaller conference school, with a compact travel schedule. 

You absolutely need to meet with the coaches of the program you're interested in and talk to them directly. Every program will have different demands, and the coaches can/should be able to put you in touch with students who have personally done what you're asking for. Honestly, the more competitive the program the harder time you're going to have. 

Personally, playing D3 Lacrosse and majoring in Architecture really worked for me. I'm sure I wasn't the best student because of lacrosse commitments some weeks, but I also think it forced me to be more disciplined and scheduled.  I think having a physical outlet was extremely valuable, and just leaving studio for 2-3 hours a day (in-season) to reset was a boon. I don't think I would have been a successful college student without athletics. 

I was on udms fencing team for 1.5 years and found it way too hard.  The men’s and women’s teams travelled together, meaning we were gone from Friday night until late Sunday, as the teams competed on different days. 

There was another arch student who somehow did ok in both activities.

It's possible. My son is attending a reasonably decent school and maintaining a good average and still competing at the national team level for his chosen sport ( xc skiing ).  Very competitive but lives like a monk.  No hanky-panky, no drinking or fun university life! But that's his choice. The transition in first year was tough as it took a while to find training regime that was conducive to his classes, rest / recovery, meals.  Flexibility was key ie early morning or late evening workouts helped and having athletic facilities that he could gain access pretty much 18 hrs a day help or track workouts under the lights etc. Also working closely with school admin and sport program directors helps a ton.  Some schools are better than others, but I found that they really do want to assist as it looks good on the school to have top athletes who are good students.  High achievers are what the schools want to promote.

I ran cross and track in college. The big challenge was being on the road (entire weekends spent going to meets) and keeping up with studio work. Other majors are more conducive with taking work on the road. I would do all of the work for my other classes and then spend my remaining time sketching out ideas. I did have one class that interfered with practice once a week, so I had to do my workout earlier in the day.

Group projects didn’t work well on my schedule.

I also ran XC and track in College. My undergrad major however was a B.A. which I hear is a less rigorous workload and by the time academic work picked up for my final 2 years I had basically decided that my priorities were my training and studio projects and that everything else came second. I'd say I spent an average of 2-3 hours a day training and while I wasn't great with time management, I always tried to start my final crit push a couple weeks earlier than my classmates (meaning no last minute all-nighters) since I knew I would want to also emphasize my sleeping and training as championship season rolled around. In general I took my sleep super seriously (9+ hours whenever possible). 

I too am currently figuring it out if it is feasible to use my remaining eligibility during my M.Arch but I know that it won't be as simple as it was as an undergrad. These thoughts/warnings/advice are helpful.

I did my undergrad while competing as a D1 athlete and it was very challenging at times.  I had to sacrifice a lot of time spent practicing when deadlines were close, but I also had a very empathetic and flexible coach who knew that school came first.  I would often lose sleep because of the extra time spent practicing and competing whereas many of my peers could use that time to work on studio work, take a part time job, or just relax.  I think you will need to have a discussion with the coaching staff to make sure they are understanding, as it can cause a lot of issues if they aren't, which will leave you frustrated and tired.