My MacBook Pro has been running awfully slow and I'm figuring it's partly because all of the files I've downloaded and deleted. I'm nervous to delete my trash can because I'm not sure if there's something in there I will need (hoarding via computer). Should deleting my trash can affect anything in a big way?
If there's anything in the trash, it's already "not being used" by anything in the computer. Empty away without a second thought.
Your sluggishness likely has nothing to do with a full trash can though, it can be a plethora of reasons.
Is your hard drive too full? (it's good practice to leave at least 20% free space)
Are you running out of RAM?
Is your hard drive dying? (they tend to slow down lots and make noise before finally giving way, always keep a backup).