Yes, Yes, Yes and Yes
Yes if you're new at rolling
Yes if you use diluted paint
Yes if you overload the roller
Yes if you're over enthusiastic with the action
The solution of course is to wear overalls and put down dust sheets and try not to do too many of the things that cause splashes.
When you get used to them rollers are no messier than a brush especially with unprimed paint and they're several times faster. Which reminds me of some film dialogue...
Mel Brooks' 1968 movie The Producers. Brooks' slapstick Nazi complains,
"Hitler was a better dancer than Churchill; Hitler was a better dresser than Churchill; Hitler was a better painter than Churchill: he could paint a whole apartment in one afternoon, two coats."
Peccavi
February 2009