you can leave it on should not be a problem , but grease the shaft splines.
There is allot of theft in my area latley so I leave it off. , as long as your not worried some one will steal it leave it on.
I had an old 140 Johnson in 1991 and some scumB*g was able to take the whole lower unit.
Hell, give em enough time they willl take an entire engine...
lesson learned there, always leave the boat right up front for all to see.