Yeah, the straps stay on.
I've had two seperate incidents of people flinging one of my wiimotes into the wall, so I encourage people to use them before something/somebody gets seriously damaged. They're rarely an impairment to gameplay (damn you, multiplayer Warioware, why do you assume there's only one wiimote?) so why take them off and increase the risk that ballistic wiimotes will break a window, TV, somebody's glasses, or whatever?
"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
*Image indefinitely borrowed from BrainBoxLtd without his consent.