There was obviously some - eg Philip Christian was in London in 17th C and his charity fed back to Clothworkers' school in Peel.
The Island was not under English Crown until 1765 but many manx would not find employment on Island and thus joined British Navy etc. The amount of linkage has not really been researched in depth - much more post 1765 but before this the smuggling activities were mostly with Scotland, Ireland and NW England.