Yes, will update on my experience in any case, it might be best to get some type of official confirmation from CS before trying in.
From instructions point of view, at least looking at Finnish sites there is a level of vagueness in the guidelines as Phuket is listed in Finnair lounges.
For a general OW lounge I'd say no change whatsoever but in a way Finnair seems to mix Finnair lounges at HEL (that are more or less clearly branded as Finnair lounges) and Finnair lounges in general (i.e. directly contracted lounges for AY customer, likely more or less affecting statusless J-pax) on their pages but it is quite clear that it is pointless to argue such nuances in Thailand with lounge agent...
I double checked the marketing codes, HEL-DOH-HEL has AY code=clearly fulfilling the terms for "Finnair lounge"=whole family in to Premium lounge at HEL, however Doha lounges are not in AY's lists -> OW rules apply (and due to the level of the lounges, considering strongly purchasing AM-access for night time layover). But for HKT-legs they do not have AY-codes hence I'd say normal OW rules will apply.