No, Ive run my boat
, and a number of others held by LLCs, or other forms of corp entities, across international borders many times with zero issues. The most Ive ever been asked for is a letter of authorization from the corp entity...and not often for that. I keep copies of the authorization letter, signed by me, authorizing me to operate the vessel in the ships papers.
, the owner (the LLC etc) is normally the named insured and additional insured parties may be added (such as the individual/captain who actually operates the boat).