Yes, Guest Services will cash Traveller's Checks in any amount on board. They will only cash personal checks for a total of $100 per person, per cruise. But traveller's checks are no problem.
Strangely though, when I wanted to write a check to pay part of my shipboard account towards the end of the cruise they wouldn't allow that. They checked with supervisors and discussed among themselves, but the rule on personal checks is that they will take them for the total amount of you bill, but they won't take them as partial payment. It had to be written for the exact amount of the final total. Strange. I know that isn't what you asked, but......I found it odd that they wouldn't allow partial check/ partial credit card settlement. But again, travellers checks were accepted as partial account payment and for cashing to have $$ for taking on the islands.