Is this correct? Is this a common issue?

Ummmm, I don't think so... our vessel sink drains just fine! Kitchen sinks also don't have overflows, and they too should drain fine, as does mine and probably yours! That's because drains need venting....

Drain venting, per se, is not related to an overflow- for drain water to flow freely, there must be air behind or above the water. If water completely fills the diameter of a drain pipe and there is no source of air behind it, the water will gurgle and flow sluggishly. In a home plumbing system, vent pipes supply the air that makes for smooth-flowing waste water. Maybe the drain size is incorrect for the flow rate of the faucet? Maybe the sink is too far from the vent?

Something just doesn't sound right.

From what I understand it's a common issue and it's an issue with me as well. Maybe not quite to that extreme, but aggravating none the less. I can't find it, but I (thought) I saved some information about a drain you can buy that's specifically for sinks with no vent. It's a venting problem. I haven't bought one yet so I can't tell you if they work. Wish I could remember the name of it. I'm sure a plumbing store would know.
Here's a couple links:
http://www.askmehelpdesk.com/plumbing/new-vessel-sink-without-overflow-drains-slow-39837.html

http://www.askmehelpdesk.com/plumbing/new-bathroom-sink-backs-up-halfway-quickly-drains-repeat-no-overflow-sink-47231.html

Monica

Thanks for the link! We will share it with our friend-- maybe it will help her plumber. But, it doesn't alleviate our own concerns about setting ourselves up for hassles. From that thread, it sounds like a lot of people have this problem, and while the thread offers several possible solutions, there didn't seem to be any solution which worked for everybody.

Re kitchen sinks not having overflows: I thought about that, but kitchen sinks have bigger drains. So it's not really the same situation.

I have two vessel sinks. No overflow, just the push down drain plug. Have no drainage issues. water drains fast even at full faucet flow rate.

It can be the screen that's causing the problem.

The surface tension of the water in the screen mesh, coupled with the "non-venting" aspect from not having a wide open overflow, is just enough to prevent the flow.

Easiest remedy it to get rid of the screen. You can do that with a different drain assembly.

Some people still have trouble with some pop-ups, in that case you usually need to add a vent underneath the sink, after the p-trap.

Some install a air-admittance valve. To me that can work only if you can install the valve ABOVE the waterline of the sink. Install it below the waterline and you could have leaks were you to have a clog/backup/valve malfunction.

I've also heard of plumbers installing a vent tube into the drain line, again after the p-trap, then running it into the stud bay and then up vertically, so the open end of the tube is above the waterline of the sink.

And I forgot to add...replacing the screen with another drain assembly is easy.

The other two options (studor valve below the sink and running the tubing into the wall) I mentioned might not even be code compliant.

I found the information I saved concerning drainage problem. I think it's basically the same thing Mongo said, but here it is...
If you choose a vessel sink with no overflow, then there is a special air vent that you incorporate into the drain line. They work great. You just have to be sure you have room inside the cabinet to accommodate the vent because it has to be higher than the drain line. They are available at any good plumbing shop.
"vacuum breaker."

a vessel with no overflow not draining fast enough.

in this very specific case, i think it is good to point out that "venting" could mean before or after the P trap.

In plumbing, venting means after the P trap.

If you had two vessel sinks (each with no overflow) connected by a "continuous waste" onto a single P trap, they would both flow well, as air in the pipe below one sink before the P trap would get displaced into the pipe of the other sink. Newbies, search on "continuous waste" to see images. Continuous Waste Center Outlet is easiest to visualize. Continuous Waste End Outlet is the other option.

If someone else more qualified wants to add to this description, please do. To add more precise plumbing terms to describe the two kinds of venting. Before the P trap and after.

Water and air have to be exchanged (displace each other) for a pipe to drain well. When it drains slow, one can increase the pipe size (which allows air in the pipe to move around the water coming down) by one size, or give the air another place to go to.

AAV Studor type valves are for letting air in, not for letting air out. They are used after the P trap not before.

Following the logic of air displacement described above, one way to solve the slow drain is to Wye in a standpipe which would then let air move out of the way (get displaced) when water comes down the drain. The standpipe could be hidden from view; it doesn't have to be in the bathroom if you have a more appropriate place for it behind one of the walls.

HTH !