OK…
IF your TRN was NOT in enemy held seas at the start of its move, then YES, one can stay on-board (but as already mentioned, if you offload in Combat, you can’t offload the otehr in NCM, even to the same territory as the combat offload)
HOWEVER.
IF there is an enemy ship in the same SZ as your TRN at the start of your move (a sub that had previously been submerged but surfaced, or you are off the coast of an enemy IC and he builds navy on his turn), then you can either just move your TRN away, or, IF you grab forces (froms somewhere else, you can NOT load in a hostile or contested sea zone), then those forces MUST offload to COMBAT. You can NEVER NCM with a TRN that starts in a contested SZ.
Another of those items in the rules, that in one game I used to my advantage quite nicely (it was the game that I was against 5 UK BB’s as Germany…)