It will work and yes, it's worth it. L glass is worth the purchase. As long as F4 will fit your needs, that lens will be great. If you need low light shots without a flash, that's not going to be the lens for you.
If you don't get it, I want it!!! It's definitely worth it, most of the used ones I've seen go for around $600
Honestly, you won't get anywhere near the quality of L glass with a non L lens.
If you were shooting professisonally, it would be an easy decision. $300 more in glass would easily pay for itself in the quality of your shots and what you would get for them.
I remember college, so I know what you mean. You just have to decide on a budget and get a lens within that budget. You can upgrade after you get a full time job. Another way to look at this is to consider that the lens is something you can have for a LONG time. L glass will go with you for many years and multiple bodies within the Canon family. Full frame and crop bodies will handle it.
$300 invested now coule be something you are still using in 10 years or more.