By all means try to get your class 2, but I would recommend you talk to an AME before paying for more than trial lessons. I am afraid I cannot see how a period of uneventful flying will play any part in determining your eligibility for a medical license. The assessment is made simply on the risk of you becoming disabled in future. I am not an AME but my understanding is that there is more than one disqualifying factor here if applying for an EASA medical. You may well be more fortunate in the US and it is worth discussing with an AME.