I don't think there is any harm in doing some of the flying in a light piston. Just to get the hang of holds and the procedures. However you should be able to do basic instrument flying before you start the IR. You must be able to fly straight and level and execute coordinated turns without having to work too hard. After all the instrument rating is more about aircraft management rather than handling. I agree that at some point in the course you should be exposed to hard IMC and that means Bristow's 206 or a small twin. Being a graduate of the Bristow's school I am biased towards doing the single IR and then doing a multi upgrade once the twin type rating has been done. I believe this used to be reflected by the IR pass rate, although that was some time ago.
However I think the major point is the availability of a Stab system. I believe a SAS would make the IR so much easier than in a floppy stick machine and is more important than the one engine or two issue.