The only reference I found about it was in Portuguese Wikipedia, and it claims that he received the invitation from the Greeks not much after the "Dia do Fico", in January 9th 1822. It means that the Greeks were only starting their independence war and where not recognized by any power yet. I really can't see Pedro leaving for a messy Greece, needing to deal with a war against the Ottomans, while the situation in both Portugal and Brazil wasn't clear enough.
By early 1822 he had no male heir to the throne (the infant prince João Carlos would die in February) and his pregnant wife would give birth to other girl (Januaria Maria) in March. The fact that his wife was pregnant was one of the reasons why he didn't accept to go Portugal in 1821, I can't see him deciding to go to Greece with her in the same situation one year later.
However, assuming that he had accepted the offer (maybe he goes mad?) than he would have made both the Brazilians and the Portuguese angry with the Braganzas. Brazil would still try to gain independence, as the elites had saw with the "opening of the ports" promoted by John VI that Portugal was more dependent on Brazil than the contrary. While this, in Lisbon Pedro would be reviled by his action and Miguel would gain more support to be the successor of John VI (also, I really can't see the old king supporting such scheme from his son). Also, he goes to Greece when the war was still in the beggining, and there was no support from the powers to the Greek cause. So, he would be in a foreign and strange country, where he didn't even speak the local language, needing to lead them in a war against a powerful enemy and without foreign support. Probably he wouldn't have a great future there.