NO!!! It wont 'fit right in'.

Your hub will only 'fit right in' a 130mm frame.

A 126mm frame will need to be opened up to 130mm. There are 2 ways of doing this, first is to set it to 130mm so the wheel drops in and out, this is called 'cold setting' and it will stay at 130mm. The second is to simply flex open the frame and stuff the wheel in. Every time you remove the wheel the frame will flex back to 126 and you'll to flex it back open and re-stuff the wheel back in each time.

Other issues to look out for:

Brake reach: Your current calipers may not have proper reach. It will depend on the frame you pick.
FD band size: Odds are your FD will be way to big. Fortunately FD's are cheap
Headset: You'll need a new one.
Seatpost: You'll more tahn likely need a new one
Stem: Yours wont fit a 1" threaded steerer. Use a threadless stem adapter.
BB: Whats the width of you C-Dale? It may not match the vintage frame you buy. Italian vs. BSA 70 vs 68