It helps. The way this works is that you download a small packet to work on and then it sends the results back and gets the next packet (also there is redundancy in case someone doesn't send a packet back for a long time for whatever reason it gets distributed to someone else)

There's no need for reacting to asteroids "on a second's notice" (that's the whole point of doing this, really), so whether you work on each packet for an hour or a day makes no difference. With a slower computer you'll just go through less packets per day.

Consider that once a dangerous asteroid is detected it will take months/years to get a deflection mission launched - so a day or a week of 'delay' on the processing side isn't going to affect anything.