Be careful .. VMS 1.0 was released in the late 1970s, we had Vax serial #1 at CMU - I want to say 1976 or 77.  Dave's Command Language (DCL - renamed DEC Command Language by DEC marketing) was originally part of an earlier RSX and yes used $ as the prompt.

But numerous systems used $ and many of the other punctuation chars as a prompt.

We'll have to ask srb, but I'm fair confident in stating VMS had no bearing on his choice of a command prompt (I'm fairly sure VMS was not release by the time he came to the Labs).   I would have expected if it was taking it from another system (which is possible) it would have been on the British ones in use at Cambridge before he came to BTL.