If your side project is really important to you, and this event derails it considerably, then you risk your memories of your friend being tainted with resentment. If it is a matter of a couple days, that is different.
You should process the emotions (by seeing a grief counselor) but you should be open to deciding to keep with your project so that disappointment over derailing your project does not morph with grief and other negative emotions from your friends dying.
A startup requires a lot of effort. If he is still excited by the idea and can work on it, then go for it. If he is finding that he is a different person, that's fine too. Everybody responds differently.
I know that with the loss of a family member, the general guidelines are not to make major choices for a year or so. If he is graduating from college, then that may not an option.
