Can I apply for a Thailand non-O visa while in Vietnam and do a border run while waiting for approval?

To save time in Vietnam you can start to complete your application before you arrive then when you get your entry stamp upload that as proof of current location as soon as you get it and submit your application within minutes of arrival

I'll explain how it works (or how it should work) and you can make your own decision

You go to a country, apply online, upload the required documents, pay and then you wait in that country until the visa is approved.

There is nothing specifically in the rules that prohibits you being in the country whose consulate you're using, applying, then returning to thailand

BUT

with that being said keep in mind some consulates will send you a request for additional documents and want copies of all the pages of your passport (blank pages too) just to check to see if you went back to thailand.

As a rule they're approving standard visas (Non-O, Non-B, Non-ED, Tourist) pretty fast at most consulates in S/E Asia, so I would doubt you'd be there more than 3 or 4 days.

The other problem you might face is getting back in free stamp 60 day visa exempt when you come back without a visa. Depending on your previous entry/stay history you could be pulled aside questioned, and/or denied entry at the discretion of the officer you're standing in front of when you go to stamp back in free stamp.

I'm not trying to scare monger, I'm explaining the very real risks you run in doing what you're asking about. It could work fine, or it could run you right off the rails. That's a decision you have to decide on your own, and no one on this group can tell you what you should do.

how long do you get in Vietnam when you go there? Most of those visas are approved pretty quickly, (certainly in under 5 working days)