Yes, but he could have grab it with something not with his bare hands.
While wearing a loin cloth, fighting for his survival against RCV, in a fire? I doubt it.
RE: The angel choosing not to harm Thomas, why did it choose to harm Susan in DM?
The difference between Thomas not getting zapped and Susan being zapped could easily be that WCV don't react to the power of faith and RCV do, but I don't recall Susan and Martin having any trouble hanging out in a Catholic church.
His ability to touch it all means that it being the Sword of Love won't prevent him from wielding it.
TheCuriousFan's question is interesting. When did the Sword stop being weakened? When Thomas recovered it or when Michael picked it up? Harry felt the Sword's power before Michael picked it up.