What would happen if the world recognised the Armenian genocide? Would Turkish government be obliged to return territory or pay reparations to the Armenians, I am really not sure. Any thoughts?
Nothing really. It might sound glib but that's really how international law works. “Recognizing” a genocide might seem important on a symbolical level but it has no legal consequences, certainly not on international matters like territory (what a can of worms!) or reparations.
What recognizing a genocide entails is not obvious either. A parliament can vote a law with a statement of fact but that's a somewhat peculiar idea and it has been criticized precisely because it has no legal effect. Parliaments do not usually spend their time voting to formally state that this or that is true.
The only way the Turkish government could be brought to do anything are the usual diplomatic/political means: complaining officially, summoning an ambassador, threatening to reduce support or exchange in various domains, declining to enter new agreements, breaking diplomatic ties, enacting sanctions, etc.