So what about the Pi3 and my NOOBS-based aupdated old-Pi2 SD card? will it run or sure or not?
It is very likely that without some action on your part that the microSD card will NOT
boot up an RPi3 or other similar recent hardware.
There is documentation that explains what to do: it involves 'transplanting' some vital files from the RECOVERY partition of a current NOOBS Installer into the corresponding partition of your old, non-functioning microSD card.
Obviously there is a risk of error during this process, so having a tested working backup would be advisable, but obviously tricky with a now broken RPi2.
An alternative might be to do a clean installation of a current release of Raspbian onto a new microSD card in preparation for booting your new RPi3. Then use a USB card reader/writer dongle to recover essential materials from the microSD card from the old system.
(On reviewing previous posts I can see that @DougieLawson has already made the same recommendation, but not at such length.)