Firstly Messor are exogenous-heterodynamic and this means that diapause is not a necessity for this species. They respond only to temperature drops to decide whether to enter diapause and will continue to develop through winter if the temperature stays warm. (As opposed to other species which are endogenous-heterodynamic, their diapause arises due to internal factors (endogenous timer) and no external conditions can prevent it.) Having said that it is very probably beneficial for a mature colony to have a few months rest from brood production and there is some suggestion that not having diapause decreases the life expectancy of the queen. (although this is something commonly said by antkeepers I don't know if there is actual evidence to support).
Also while speaking of Messor diapause, since they are a Mediterranean species they only require around 14-16c to view it as cold and do not require putting in a fridge as you need to do with more northern species.
The first question would be what conditions has the seller been keeping her in? If they have been keeping her cold waiting for the sale then it's going to take her a few weeks to decide that temperature are warm enough to start egg production. Depending what temperature she is at now (you don't mention) she might still not think it's warm enough.
Next thing, you must never put your queen or colony in a sugar water test tube, this will kill them, the test tube should always be fresh water, preferably bottled or filtered as tap water in some countries has chlorine added which while safe for human consumption can build up in insects and kill them. Ants not having access to a fresh drinking water source is the fastest way to kill a colony, even when they are in a nest you still need a drinking water source somewhere in your set up.
Yes you could feed a tiny (and I mean really tiny, no bigger than the head of the queen) drop of honey on paper or foil so that you can remove again after 24 hours if she doesn't eat it. You've no real idea when she was caught, how long she's been kept and at what temperatures etc. so she might be low on reserves.
Finally Messor are a really hard species to start from just a queen, once you have a colony started they are one of the easiest species to keep but the founding stage with just a queen is really quite tricky. They have a tendency to not produce and to just roll over and die for no good reason. They are very susceptible to disturbance, especially vibrations but also sudden light level increases, you should try to leave her alone as much as possible, checking even less that you suggested. She has also been through a lot of stress recently as she got shook about by what ever delivery method was used to get her to you. However don't be too surprised if she doesn't make it, as I said single Messor queens can be hard to get going. (if you are new and do this again, I recommend buying a colony with some workers already for this species).
TLDR
Offer tiny sugar once, then put away, leave alone and cross your fingers.
