Given the amount of snow this year (which still appears to be falling…?)

NO

Depends why you're asking! All but the very highest trails will be rideable, and almost all the road passes will be open by the end of June. Snow line on all aspects is now around 2000m (from a quick look out of the window!) and patchy higher than that on South slopes.

On the other hand, if you're going into the high mountains for glacier travel, etc. then there will still be plenty of snow!

savolyeres, verbier

Thanks – I'm heading to Chamonix for riding, mainly altitude seems to be between 2K and 2.5K – I'm sure it'll be fine

Thanks – I'm heading to Chamonix for riding, mainly altitude seems to be between 2K and 2.5K – I'm sure it'll be fine

Should be fine – you'll come across the odd snow patch in sheltered hollows at altitude, but nothing that'll spoil your riding.

mrmo, climbed up to croix de cour on savolyres about a week ago, had to push for a couple of mins where the piste crossed the road, the rest was clear, loads of snow on the north facing side though.

and almost all the road passes will be open by the end of June

I think the very important word here is ALMOST.
Temperatures have drop quite a bit in the last fortnight it has snowed 60 cm in chamonix, all local col and passes will probably remained at least covered in snow if not close for the summer. Cross fingers, but the motorcycle season looks like compromised 🙁

oh, that doesn't sound good…! Do you think it's likely to have cleared up around the Col de Balme/L'Index lift etc. (c.2,500m alt.) by late June then or am I stuck riding below the treeline?

late June is as good as anytime for stuff at 2500m to be clear, there'd certainly be no advantage to waiting any later. It can snow down to 2000m any and every month of the year. In the Tarentaise the snow is actually really high up for this time of year. There's nothing to stress over at this point for sure, I'm sure you'll have fun and be fine.

Temperatures have drop quite a bit in the last fortnight it has snowed 60 cm in chamonix, all local col and passes will probably remained at least covered in snow if not close for the summer.

I think that's very unlikely. The current weather isn't particularly unusual (much like May 2 years ago, which followed a much snowier winter).