
I did this for several months actually. My main character, Sounsyy, was on Hyperion doing PVE content, endgame raid, crafting/gathering FC, etc but then I had an alt that I transferred to Balmung, named and fantasia'd to a copy of Sounsyy just for roleplay. As I said I did this for several months but, for me, it was rather unsatisfying on the RP front. I was mostly inclined to complete things on my main character and seemed to only log into Balmung occasionally or for event RPs.
I'm not very good with alts, and don't have a ton of time to dedicate to them, but even with both my characters on Balmung now I've noticed that I can set aside more time for each and get RP/PVE/whatever done more fluidly. So it can be done, and it can probably be done better than I was doing, but it's not easy. You'll end up favoring one character over the other usually, and in my case that was the PVE side.
I'm not very good with alts, and don't have a ton of time to dedicate to them, but even with both my characters on Balmung now I've noticed that I can set aside more time for each and get RP/PVE/whatever done more fluidly. So it can be done, and it can probably be done better than I was doing, but it's not easy. You'll end up favoring one character over the other usually, and in my case that was the PVE side.