A reluctant 'yes', on the basis that:
1) Defeating ISIL in Iraq, where the ground they vacate will be controlled by the Iraqi government or the Kurds, will be made easier if we can also attack ISIL in its logistic hinterland of eastern Syria. On this point, if ISIL try to make a big issue of a British vote to extend operations into Syria, we have an immediate strategic communications coup. ISIL claims to have established a Caliphate and does not recognise the border between Syria and Iraq, so according to their own narrative, the UK is already bombing them. As such, a vote in favour of action should be irrelevant. If they claim it changes things, it means they actually recognise there is a border, which undermines their claim to power.
2) I am not convinced that we need a credible follow-on plan in place for Eastern Syria. Nothing could be worse than what already exists there. So the lack of a plan is not a reason to deny ourselves the potential benefits of my point 1).
3) Our military commanders have enough sense about them to keep our aircraft away from potential conflicts between Russia and Turkey near the Turkish border.
4) I am not too worried about mission creep. Everyone knows that Western troops would be entering an IED- and ambush-filled bloodbath, would struggle to gain local acceptance and would almost immediately have to go into self-protection mode to assuage public anxiety at home. This would render them militarily ineffective, as seen in our last two big Middle Eastern ground wars. I think the military leadership is sensible enough to see this now (finally) and will keep its ambitions strictly limited.
But I am under no illusion that extending our mission into Syria will either be decisive militarily, or contribute to ending the long-term conflict. Doing that requires us to look again at our relationships with Saudi Arabia, Turkey, etc for reasons that I have bored on about elsewhere, not just for the good of the region, but for the future of open western societies as well.
5-7.