No, the user would complete the transaction on paypal and be re-directed back.
If you do set it up on your site you're going to have to set up the whole checkout script in something like php, use a merchant gateway to bill cards and then have to deal with ssh certificates, another expense as well. You'll have to do a good job of it as well to avoid looking like a scam site.
All of that is going to add extra expense and discourage users like myself donating. Ive donated to a few sites before using a couple of pounds out of my paypal balance. Ive never donated to a site using my credit card.