You definitely want the upgrades. I don't think it's even possible to survive without one but I'm happy to be proven otherwise. After a couple of upgrades you should find yourself blasting through heaps of bad guys with ease.
I set the game's timer to 6 minutes for two reasons; I wanted to emphasize that the game in its current jam entry form is meant to be played in a quick run without getting too involved, but also because the music track was 6 minutes :))) I'll take the fact that you wanted to play more as a compliment, though :)
Thanks for playing and the feedback.