But then what about with Romulan and Klingon ships, during that period when the ship is cloaking, and the shields have dropped, but the cloak hasn't quite kicked in completely, and it is still possible to target them? I guess it all comes down to calculated risk, and whether or not the MVAM was deemed to outweigh the risks.
I think that's a much shorter period of vulnerability, and with fewer potentially problematical variables.
Of course, intrinsically, the very idea of a cloaking device for a spaceship is even more ludicrous than a multipart ship could ever be. The latter is just overcomplicated; the former is a thermodynamic impossibility. Ships produce heat, and in space there's no way to dissipate that heat except by radiating it outward, which produces a detectable signature. A ship that could cloak all its energy would cook its own crew. If I could expunge cloaking devices from the Trekverse, I would.
It seems like you are assuming that each piece is designed to run completely separate of each other for extended periods.
Yes, but that's exactly my point: That while a ship designed to function in both a unified and separated mode may be basically functional, the three partial ships won't be as functional or capable as three complete ships. If you need three ships, the simpler engineering solution (and the first rule of engineering is "Keep it simple, stupid") is to
build three ships, rather than giving into the allure of flashy gimmicks and inventing some cutesy way to make one ship that splits into three pieces.
MVAM seems to me to be no more than a glorified saucer separation. 3 pieces instead of two, and each has a warp drive instead of only one of them having it. The saucer of the Enterprise-D didn't have 3 sickbays. It had only one bridge per section as well, it didn't need each section to have it's own dedicated backup. And then what happens if the Enterprise-D loses one of it's section while separated? It doesn't seem all that different to me.
The key difference is that in a saucer separation, the two parts aren't meant to function in tandem in a combat situation. The saucer is meant to be left behind somewhere safe while the battle hull -- only one ship -- goes into combat. The saucer isn't meant to be a functional starship on its own.
Even so, it's not the design I would've gone with. I feel that if they wanted to have a largely civilian research vessel with independent combat capability, it would've been simpler just to send two ships out together. Two specialized ships are going to be more effective at their specialties than one general-purpose ship that can split into two semi-specialized halves. Might've been more dramatically interesting, too -- imagine a TNG with science-ship captain Picard and defense-ship captain Riker clashing over their different philosophies and approaches to a given crisis.