should we ask ATC if they want us to squawk 7700?
AFAIK ( in the UK anyway) squawking 7700 is definitely "a good thing" because it may well alert the controller(s) running in the adjacent (as in lower) sector that you're about to plunge into their airspace.
UK advice here:
http://www.ead.eurocontrol.int/eadba...2012-11-01.pdf
In busy, highly sectorised airspace, controllers may adjust their situation displays to filter out aircraft in adjacent sectors, which will
be separated vertically or horizontally from aircraft in their own sector. This is done to prevent clutter on the controller’s display. Selection of
the emergency code 7700 will override the display filter and highlight to all controllers the emergency state of the aircraft, whether or not the
aircraft is in their sector (including vertically). This function allows controllers to act quickly in providing separation from an aircraft in
emergency descent as it passes through their sector. The prompt selection of 7700 is of paramount importance