Yes! As a matter of fact, I think someone just suggested in a similar post that you consider putting a bottom on it and raising the whole thing a couple inches.

Just drill drainage holes and you're good to go!! If you wanted to put casters on it you could push it around to get the most of the sunshine.

Well, I wasn't going to put a bottom on it. I wanted to pile the soil straight onto the concrete pad, using that as the bottom of the bed. Would that be alright?

You might want to put some gravel in first to help with drainage.

It has worked well for me. I've got three 4x5 raised beds on top of a concrete pad in my backyard. I used cinder blocks 2 tiers high and then put about 1 1/2 to 2 inches of gravel in the bottom. I put landscape fabric over top of the gravel and then filled with compost/soil mix.

This year will be my third season in them.