No, but you can (and most shops in my experience do) ask things like how long they've been certified, and how many dives they've done, etc.
When they're PADI certified (PADI is the agency for the masses, which means their minimum standards are pretty minimum), have been certified 5 years and have 10 dives, you should have a pretty good idea what to expect from them.
I've been to a number of places (mostly shore diving destinations) where a "check out dive" was mandatory before you were turned loose. The given reason was "to get your weights right" but you can be assured it was also a way to see who had what skills.
And most all dive shops that I use make sure that someone new to their shop goes someplace easy to be checked out. For example, one of the "bucket list" dives on Cozumel is The Devils Throat. It's a tunnel about 60' long, that starts at about 80' and comes out at 130' or so. Technically, OW divers should not be in that sort of overhead environment, but it's common practice for OW divers to do swim throughs. A swim through of that length, though, especially at those depths, is a bit sketchy for OW divers. Everybody wants to go do it. There are a couple of dive shops who will look at your card and say 'get on the boat', but not many. The shop I use there (Aldora Divers) and most others, will not take you there regardless of what card you show them, until you've been on an easy dive or two so they can check out your skills.
If you look at a site map for Cozumel, you'll notice that all the sites are on the west side, south of the town. There are actually excellent sites to the north, and on the east side, but they are all considered advanced dives, because of current, depth, etc. One example... if you go astray at any of the southern sites, you're going to drift along the coast, past tons of boats, or you could paddle your way in to shore. If that happens on the north shore, the next thing you're going to see is Cuba...
Aldora is the only shop that does east and north sites. On one trip, I wanted to go north. I went into the shop, and the fellow was new. I handed him my cards (Trimix, Hypoxic trimix, Cave...) and he insisted I needed to do some south sites first. I was willing, because those are all fabulous sites. But Memo (Memo and Dave are the owners) came through and straightened it out.
Honestly, I would avoid a shop that didn't do this sort of thing like the plague. Or cattle boats.