That Voyager was at DS9 before looking for Chakotay tells us nothing of where Janeway and her then-senior officers were before their mission began.
I'd say the fact that Janeway visited DS9 and then embarked on a mission specific to that area of space would almost certainly involve her discussing local matters with Sisko, or at least reading his reports on those. And the Dominion issue would definitely arise, as it was a very clear and very present danger at the time. Indeed, the threat was probably at its highest at that time, because Starfleet had every reason to overestimate it!
However, by the same tokens, the discussion between the COs would no doubt remain top secret. And while the information would gradually be leaked to the crew of the Voyager
, the EMH would be at the very bottom of the list of recipients. Far enough down not to hear anything until "Message in a Bottle", though? A bit unlikely, considering how curious and chatty he later became...
As for programming the EMH to deal with Jem'Hadar weaponry, I don't think Starfleet would know anything about such things yet. Nobody had been hit by Jem'Hadar light arms in "Jem'Hadar", and none of their weapons had been captured. In contrast, their ships had been in combat with Starfleet assets that had survived, so it's not unexpected that Paris in "Parturition" would have access to a crude simulation of Dominion ships.