Replying here too so that those who dont see the other reply would get this information too.
Yes, you can complete the game without towers, I realised while playtesting that it is probably doable, and considered preventing it, but came to conclusion that since those defensive towers are a bit hard to figure out, due to no good hints existing yet, it would be better to let player be able to get through the game, although the alternative way is the boring way, and missing half the fun of the game, since main fun was supposed to be in balancing the power between different colored defensive towers and balancing between whether to use them to passively damage enemies, or use shooting.