Silly Question About Chapels and Barbs

From time to time, if you spy buildings in barbs, you fine one that still has a chapel, presumably a remnant from when it belonged to an active account.
If one "supports" said barb (in order to hide troops, whatever) does that barb's chapel still function? That is, does the strength of my troops remain the same as if they were supporting an active player's village which happened to contain a chapel)?
As noted in the title, a silly question but one I have been curious about since I first spied a barb and saw a chapel.
 
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