I'd say a firm "no" at the moment. Most things in space flight have a lot of lead time, so if it takes a while to run a bunch of calculations and/or simulations to plot a burn or something, that doesn't usually matter. The majority of constraints with spaceflight are physical: how can we bring enough equipment, fuel and consumables to keep everyone alive for the duration of the mission and to do all the required manoeuvres, without making it impractible?

Having a better computer doesn't sidestep the 'tyranny of the rocket equation': the heavier your craft, the more fuel you'll need to burn to perform a manoeuvre; but bringing more fuel makes your craft heavier, so you'll need to burn even more...