Yes, you can do that. You would be purchasing a new license at that time, which would cost you roughly $US50 (for basic MATLAB) or $US100 (for the bundle), plus roughly $US10 per toolbox that you purchase at that time.
Probably it would be less expensive to renew the software support on your existing MATLAB license, but not always.
In particular, if you plan ahead of time and know that your PhD will need a number of toolboxes that you do not already have, then it can sometimes turn out to be less expensive to go for a new Student Suite later so that you can buy those toolboxes for roughly $US10 each, instead of $US25 each that it would cost to add the toolboxes to an existing license.
But if you already have all or most of the toolboxes you need, then typically renewal of your software support would be less expensive than purchasing a new license.