I have a filtered and cycled 2.5 gallon but honestly if you practice good husbandry you should still be doing 2 weekly water changes on a 2 gallon so its up to you.. the only thing filtering/cycling does is keep you from having to do 100% changes.. if its cycled you can do 2 50% changes a week and vacuum the gravel/substrate.
I would do it (but I like all my tanks to be cycled).. I hate doing 100% water changes so for me getting a filter and cycling is worth it.
I personally say yes. A filter cuts down on water changes and keeps the water more stable. Ehiem makes a small internal filter for around $13. I also bought one from PetSmart by Tom's Aquarium for $15.99. It's used to up to 5 gallon aquariums and is worknig great so far. I only use the sponge insert. I removed the carbon because I also have my tank planted with live plants.
I don't use any of the filters in my tanks. If you don't use a filter, you're going to have to do more water changes. So if you don't have the time to clean the 2G twice a week 100% than you can get a filter.