"They boarded the boat enthusiastically [or 'with enthusiasm']" should be accepted. It's a more natural English expression. For one thing, "get on the boat" sounds rather informal. An announcement at a terminal, for example, would tell passengers to "board the boat" not "get on the boat."
I am not sure why someone down-voted you. Although 'climb' has 'grimper', when talking about rock/tree/mountain climbing, 'monter' is used with the sense of 'climb on'. Of course, it depends just how big your yacht is. I tend to 'land' on mine.