If I have Bronzong with the "Heal Block" Ability in play, can Pokemon Center stadium be used to heal any Pokemon in play?
No, you may not.
Source: Next Destinies FAQ (2012-02-09), TPCi Rules Team (2012-02-09)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS4_9
WOTCB1_85
WOTCPR_40