Is it okay to not varnish wooden furniture before use?
Not finishing wood is perfectly fine.

It will be more prone to collecting dirt and stains than finished wood, but if you don't mind that, it's still fine.

If your budget allows, you can also apply finish yourself, some of which are quite inexpensive and relatively easy. But you don't have to. 

If at some later point you feel that the dirt and stains acquired are annoying, you can sand the wood to remove them, and apply finish then if you want to; or simply repeat as needed.