I'm not sure I understand the "lumping" procedure. However, the bottom line is that by changing the constraints, you change the feasible region, and therefore you also change the solution to the problem. The only way I can see that being useful is if the lumped problem is a decent heuristic approximation to the original problem for some reason. By solving the lumped problem, you could then maybe obtain a better initial guess, which could be used to solve the original problem in fewer iterations. There is no way to predict in advance how effective this will be, but it is is something you can always try yourself.
However, given that this is likely a spin-off of your earlier post, I really wonder if you're barking up the wrong tree by trying to eliminate variables. Do you know yet whether the slow performance is because fmincon is iterating endlessly, or is it just because each iteration itself is costly?
Six hundred unknowns is not a small problem size, but not really a huge one either, and shouldn't take too many iterations to converge. It's a size that can usually be dealt with pretty well, as long as you take care to implement the objective, constraints, and their derivatives efficiently. Part of doing so means not relying on MATLAB's default finite difference derivative approximations. You have to start getting into the Optimization Toolbox's options for implementing your own analytical derivative calculations. Where a Hessian calculation is required, you also might want to take advantage of options like HessMult, HessFcn, or HessPattern.
