Considering Tampa's goalie depth (WTF Yzerman), I'd imagine they'll do something to address it if Vasilevskiy is out longterm.
That being said, I'll bet acquiring a starter level goalie that would potentially put them over the cap now or when Vasilevskiy is healthy again is at the bottom of the list.
They probably ride Domingue for now. Contrary to what was said in the OP, he hasn't been "hot garbage". If you look at his game logs, he's been decent outside of a 7-1 blowout.
If they add someone this early in the season, they'll likely look at other options before they cough up assets or draft picks to open up cap space to bring in Howards salary. They could:
-Give Eddie Pasquale a look. Outside of the start of this season, he's been pretty solid at the AHL level since falling off the radar after missing the entire 14-15 season.
-Wait to see what Carolina and Philadelphia do to address having 3 waiver eligible goalies on their roster.
-Try to trade for an experienced goalie another team has in the AHL (IE Forsberg, Montoya, Hutchinson).
-Kick the tires on Steve Mason or Kari Lehtonen, who are still unsigned UFA's
Most of those will cost them anywhere from just a small amount of cap space up to a conditional draft pick.
Have to wonder too if Tampa would rather hang onto cap space and assets like a 1st rounder so they can go "win now" at the deadline and get into the Panarin/Stone/Duchene sweepstakes before a cap crunch closes their window in the next couple years...
And speaking of that cap crunch... I never really looked too deep into Tampa's cap picture but holy hell.... The apple sure doesn't fall far from the tree when it came to Yzerman handing out NTC and NMC's...