Have I ever been questioned by authorities about clearance?? Let me tell you a true story .
I was driving a private power vessel not on charter with friends aboard to Virgin Gorda from STT on a very rough, bad weather day - I went up the S.side of St. John and in the lee of Norman Is. slowed down to idle - in forward not neutral- to rearrange things and let the passengers move around a bit, smoke and get a beverage - and was boarded by BVI Customs almost immediately - the vessel was not stopped, moored or anchored and I was at the helm and underway at all times until they hailed me.
They went all over the vessel, checked everyones documents and boat papers and assessed us over $500 in 'fines' or said they would seize the vessel and take my passengers to jail and arrest me as Captain for failing to clear in.
I tried to explain that we were en-route to VG to clear in as our destination and had only slowed down, not stopped, to rearrange things in preparation for the passage after some rough water and wet weather on the 1st part of the trip.
They said that since I slowed down just outside the Bight I was planning to enter there and had not cleared in - that was not my intent but could not convince them of my plan to go straight to VG and clear in there.
Lets just say they were less than polite and my passengers actually felt somewhat threatened - I am a long time resident of the USVI and a licensed Captain for decades here but felt my fighting them in Tortola for the rest of the day if they seized the boat would be futile and expensive even if I was somehow declared innocent so we all pooled what cash we had and they settled for about $550 and -- gave me a receipt and clearance papers and a stern warning about how wrong I was and just lucky this time not to be arrested.
The day was ruined for my passengers for a VG trip and they just wanted to go back to the USVI - after going into the old Bones on Norman for a few drinks - paid with a credit card as we had only small change left in cash we returned to the USVI.
As to the OP question: Would I try to do the International trips illegally?? I suggest not.