The annexation agreement does not include any language regarding secession. Neither does the state Constitution. There are the usual platitudes about the people being sovereign, but we saw how well that played out in 1860, didn’t we?
One of the other commonly cited “quirky facts” about Texas, that it can subdivide itself into up to 5 states at any time, is actually found in the annexation agreement. Of course, the US Constitution also states that any other state can split itself too. The difference being that the annexation agreement says Texas just needs to get permission from Texas, while any other state has to get permission from its government and the US Congress.
So, can Texas secede? Just as much as Virginia and Georgia can and no more. Good luck with that, Governor Perry.