I’ve been using tubs for Cross and road for many years, the answer you’re looking at unfortunately is, it depends.
Tubs can deflate slowly, they can also just pop and hit the rim, depending on which make and model of tub as some have latex inner tubes stitched inside (Dugast, Challenge, FMB, some Schwalbe etc) some have a vulcanised chamber (Tufo, Clement, some Schwalbe). either way the tub stays stuck to the rim so allows some control of the bike unlike a clincher that can come off the rim with no air in it.
The former can usually be fixed by unstitching, patching the tube and restitching (not a road side repair) but don’t like Latex solutions, such as Stans as it can ruin the latex tube inside after time. The latter are pretty much wrecked if you slice them but you can use sealant in them to prevent thorn punctures etc.
Switching between cross and road tubs isn’t a 5 min job if you want either to stay stuck to the rim during use (you DO by the way, it hurts when they come off) but can be done overnight safely enough. In an emergency you can swap a tub at the side of the road/trail if you have one, but spares are bulky and you’d have to ride very carefully back as it won’t be attached very well other than the air pressure.
I love tubs for racing and wouldn’t use anything else by choice, I’d not leisure ride on them by choice and am always grateful that I’ve had no issues when I just ‘nip around the block’ on my best wheels.