Really depends on how much work you put in, and also probably genetics. And whether anything else is wrong with you.
Two cases that show how weight alone is not really a determining factor: Amberlyn Reid used to be nearly immobile in the upper 500s because she was not getting up and moving. Then she got up and made a concerted effort to regain her mobility, and she did. She is probably about 30-40 lbs lighter now (maybe less) than she was at her peak, but seems to have no mobility problems. Another example is FatMissT. She is around 800lbs (or for sake of argument - i.e., so that nobody comes and tries to say she no longer that size as we have not had a weigh in in a hile - she used to be over 800), and she gets around great.
My 600 Pound Life is a great place to see the variety of mobility at that weight: some people get around fine, and others cannot get out of bed. All comes back to how mobile they stayed while they gained the weight - and a lot of that I think is if they don't have someone to enable them, then they have to move around just to survive (like MissT) - then they can stay mobile at incredibly high weights, when others who weigh hundreds of pounds less have been allowed to be sedentary and lose their mobility.
All that said, this is a really interesting question, and I am glad you posed it. The related issue I always wonder about is how women who are not into gaining feel when they eat themselves into needing a mobility scooter and how that does not become the wake-up call that they need to lose weight (as it is for a lot of women - for example, I would love it if my wife got that big and stayed that way, but I know that if she ever did get big enough that her mobility was compromised, even a bit, she would be going in for WLS, which would be a fate worse than death). There's a woman I know who has got to be in the upper 400s - she fluctuates and may get into the low 500s, though it is hard to tell exactly how big she is - and I know back in college she was probably around 300, and I would love to know how she allowed herself to get as big as she is and needing a scooter (she was already this big when we met her and her husband - man, I would love to wife swap with him!). If only I could ask!