In most woody plants (and so I presume it's true with citrus/Poncirus as well, but have no direct proof there), it is the scion that controls growth vs. dormancy, not the rootstock. So with a citrus scion on Poncirus roots, those roots should "think" it's summer, even in winter. Certainly, in Florida, which gets rather warm weather for much of the winter, if you put lemon or lime on Poncirus, it will continue to grow quite happily throughout the winter, without a pause.
On the other hand, oranges or grapefruit on Poncirus or some citrumelos do tend to go into a deeper dormancy in winter than they would on some other rootstocks, so there is some sort of rootstock effect happening there.
But in any case, no, growing a poncirus-rooted tree warm in winter definitely will not kill, nor even harm, it.
Malcolm