I think that the GoDaddy support staff are probably encouraging the switch from your current email solution to Office 365 because it is a superior product? I don't know what you are paying for your current email solution (or if you are paying anything). I have seen and migrated users who now pay around the same of Office 365 and features for around the same price of their old solution. I don't know if that is your case but I do know that I'm also advising a switch when I'm asked.
That said there is no reason why your current setup should stop working? I assume you followed the Thunderbird: Set up email steps? Those settings should still work? Hope that helps?
...turns out that my two cents is worth less or more depending on the current exchange rate.
roy darling *my posts seem a lot shorter in my head