I don't think so. If he suspected Valeris of treason then his behavior makes no sense whatsoever.
Why not? Spock is giving out nuggets of (dis)information in select company. Sometimes only Scotty and Valeris are present, sometimes only Chekov and Uhura, and so forth. Tracking the nuggets would tell Spock volumes.
One thing that's rather strained is the fact that Valeris recorded Kirk
"Recorded Kirk"? Why would we think this?
The court quotes
Kirk's log as the source for the recording. If the court could not have access to Kirk's logs, then this would have been brought up immediately in Kirk's defense.
Valeris merely tipped the Klingons off as to what to look for in Kirk's logs. This does not call for prolonged or determined eavesdropping: she merely mentioned something she overheard, and would probably have overheard any number of racist slurs had she happened to be at the door at some other date. Or so she would assume.
It is furthermore unlikely she intended the Klingons to make any use of this in the court. Odds are she just had some free-flowing conversation with her Klingon spymaster and mentioned Kirk's compromising feelings, and the Klingons jumped at the chance, not understanding the risks, or considering them worth their attention.
I love TUC, but the idea that somehow Kirk got arrested by the Klingons, put on trial, and shipped off to the prison planet without the Klingons ever detecting the tracking device on his clothing--or Kirk ever changing clothes--is not something you want to think about too hard.
Well, what Spock placed on his shoulder was a patch of "viridium" - obviously the name of a substance, rather than of a device. And once placed, the patch changes shape from shot to shot, suggesting it indeed is a stain of some substance. So
@Discofan has it down pat: the means of tracking was inserted into Kirk's shoulder, rather than into his uniform. And it was just an unexpected bonus that the Klingons let Kirk keep his jacket and thereby maximize the dosage carried on and in his person...
Timo Saloniemi