You better believe it. Money is money. I don't think it makes you look cheap.
I'll pick up all kinds of it. Paper and change. I do tend to avoid pennies, unless I feel like saying that chant: "Find a penny, pick it up. All day long, you'll have good luck." But even if I do and keep it, by the next day, I have no idea what I did with the penny.
Been thinking I need to collect enough to bundle them in those paper things but I keep forgetting.
Bonus: The most I've found was a $20 bill when I walked home from the bus stop. It was raining that day so it was wet, muddy and when I opened it up at home--cause it was folded up and junk--there was an earthworm just lying in it. But I still kept it, just tossed the worm back outside, cleaned it up and there we go.