I think lawyers are also not sure about it. They are pretty much divided.
But, i remember when i was doing my research, it said unauthorized employment on h4 is not allowed. Since, your wife has authorization as well as h4 that should be perfectly fine. My wife also has h4 and she is working on tps ead, and her company lawyer said it is perfectly fine.
Logically thinking, if working on TPS EAD violates H4 then why not H4 EAD after I140 approved. So, my conculsion is if you have authorization to work it should not matter.
For F1 it may matters, because F1 has some rules of credit. So, if you take proper credit and works 40 hours then it also should not matter.
This is my suggestion you can look through some of the lawyers or murthy as suggested by edipre.
One of my friends brother in law get h1 approved (no consular processing). He worked on cpt for few years and on December 2015 he left cpt and was on TPS (he got is tps ead but tps was not approved yet). On 2016 he got his h1b picked up in a lottery and approved as well.