It would most likely not get past Google's board. And investors would crucify them for paying that kind of premium for a stalled social network (aka don't get the incremental benefits of growth via network effects). They would be left with 1) increase revenue/user or 2) cut costs.

Periscope doesn't fulfill the "toothbrush" principle, aka stuff that you use every day. That's how Google does M&A. Their corporate development people have talked about it publicly.

Also, the shares turnover every 26 days given that about 26MM shares trade every day. Hard to say that a majority of the shareholder base would not accept a 40% premium.