No. The information being securely stored does not mean users wouldn't have to turn over the information. However usually FoI doesn't usually apply to instant messaging anyway, I think.
Judging from http://www.ucl.ac.uk/constitution-unit/research/foi/countrie... it is already not useful. However theoretically, yes. It is hard to discover which encrypted communications are potentially relevant, and if the officials in question are doing something wrong then they have no cause to cooperate.
If they're subject to records retention requirements, they should be retained anyway; and if they're not, they're in the same category as things like phone calls which are currently ephemeral.
(Note that in first world countries phone calls will be digital everywhere except maybe the last mile, and GSM and upwards are digital to the handset)
End to End encrypted does not mean the messages have to be stored and retained encrypted and inaccessible. I imagine the responsible sysadmins have figured out something to follow retention laws.
You're not supposed to be able to access any and every government communication. You're not supposed to know what the nuke codes are, or when there's an undercover mission in progress, or [insert punchline here].
Presumably, if there's an investigation, they just force the government employee to give up the keys.
And this is somewhat okay. Though in my opinion there should be some way to lawfully intercept, this brings us back to the same dilemma as with private messaging.