I don't have an answer for the title question since I found out I was having multiples when I had an ultrasound (it wasn't on my radar at all at the time, so it was a shock, though nurses & midwives commented that it explained some things like why I was so intensely sick, though of course hyperemisis is not limited to multiple pregnancies!)
I guess without issuing dire cautions, I could say that positive outcomes in twin pregnancies (in terms of avoiding complications, going to term, healthy birthweights corresponding to normal singleton sizes for gestational age) tend to correlate with certain things such as a significant & early (by 20 weeks) weight gain and a diet that specifically supports twin pregnancy needs (such as increased weight gain & early gain, significant protein, lots of water.) I'm not sure that I'd have focused specifically on drinking a gallon of water a day (at least this was my target & I kept a daily supply in the fridge to stay in touch with what I WAS consuming) had I not been aware. Same with the protein, although my natural aversions & tastes did guide me in some important ways (though I didn't want any dairy, which limited my protein options somewhat in terms of how some folks meet their requirements.)
An early ultrasound during the window when they still can accurately count the individual layers of the membrane(s), that can definitively determine chorionicity can rule out potential problems for some twin types (by ruling out that twin type) but there's usually some other reason for an ultrasound that early on (and detecting twins is a by-product.) So if you are not generally planning on u/s, likely you miss that window.
It's true that chronic TTTS (twin to twin transfusion syndrome) can develop by or before the "common" 18-20 week ultrasound, and it's true that knowing about it through monitoring & measurements (visualizing the bladders, seeing individual fluid levels & how the dividing membrane "behaves" between the twins, monitoring growth and noting discrepancies between the babies that equal one growing "at the expense of" the other or whether they are generally keeping pace) makes it possible to manage the situation and improve outcomes. So knowing can help change things, and can make further intervention possible if needed. And as far as I know, only ultrasound would reveal situations when a more extreme intervention (such as the laser surgery mentioned before) could help. And yes, it could save lives. It's more common to monitor FOR TTTS, though, not to actually diagnose & see it happening (but avoiding ultrasound could mean missing the development of something that could have been monitored, managed, and perhaps surgically addressed if need be.)
For mo-mo twins, I'm not sure that knowing their status prevents anything until you are beyond a certain point where actual intervention could be possible, but once they are viable it could be possible to deliver them early if they were in trouble (again, detected by ultrasound) which makes some special complications avoidable. And maybe adjusting activity to reduce risk if they are revealed to be problematically entangled (with bedrest/positioning and monitoring of the situation) could prevent a tragedy.....I don't know what is typical for a mo-mo pregnancy. (And the chances of conceiving monochorionic/monoamniotic twins are statistically low!) But it seems that before a certain point, knowing the mo-mo status by ultrasound would not be specifically life-saving (though it could be later on.) And knowing about mo/mo status would influence birth choices, which could DIRECTLY affect survival of the twins in that very rare instance.
Chronic TTTS is more of an issue (if you have identical twins and if they share a single placenta) or at least less remote than the mo/mo situation, and is something that can present earlier, and something that can be managed (not merely monitored) if it is detected.
And more generally still, supporting twin pregnancy through (primarily) dietary response is something that it helps to do early, so knowing about the twins can make a perhaps tangible difference (in outcome) that way. I guess that depends on what kind of dietary habits you already have in pregnancy (for example, if you happen to follow the Brewer's diet, your protein intake is closer to recommended levels for twin pregnancy, though I think it still takes a fair bit of tweaking.) This is not particularly conventional thinking, though, as some doctors don't even mention protein to mothers known to be carrying multiples, let alone recommend or advise a significantly higher weight gain, or emphasize that ~20 lbs or so of the total gain should ideally come in the first half of the pregnancy.
But as far as the actual question, (not the aside about whether ultrasounds are advisable when you suspect twins), I'd think that measuring and palpating could give you a good idea, good enough not to be surprised at birth. Listening for the heartbeat (however you do it) and having the midwife check for another rather than just settling on the one she finds first as "it" could help to answer the suspicions, too.