Can the Paladin be summoned mid battle?
Yes

See this paragraph on p19 of the rulebook:


  Order is important. During battle, your rating on the Evilometer can
  change. This might make the paladin choose a different dungeon (as
  explained in the Paladin section above). The paladin will move
  immediately (along with any Damage Counters that are on him) so it
  is possible that the paladin will fight in multiple dungeons in the
  same round. Once the paladin is eliminated, however, he will move no
  more, regardless of the Evilometer.


The Paladin's justice is swift - if you become the most evil player at
any point, he will swoop down to punish you at once!  I believe I read
the game designer saying somewhere that you know you've gotten really good
at the game of Dungeon Lords when you are deliberately manipulating the 
Paladin's movements - e.g. sending him to trash another player's Dungeon,
but then having him come back to yours with a few damage counters on him,
so he's easier to defeat.  I think it's very hard to pull off stuff like that,
though!

EDIT: Regarding whether the Paladin can enter play when  a player crosses
the "evil threshold" for the first time in the year during a battle, I see
no reason why not.  Here's the rules from the Paladin section:


  If your Evil Counter lands on or rises above the paladin space on the
  Evilometer, the paladin sets out to attack your dungeon. Take the
  Paladin Tile from the Central Board and put it in the large space near
  the entrance to the dungeon. The paladin will always be at the front
  of the party. Any new warrior will push ahead of everyone but the
  paladin. The paladin himself is a mighty warrior. And a priest. And a
  wizard. And even a bit of a thief. For the purposes of the rules, he
  does not count as any of these, but anyone who faces the paladin will
  realize that he is an adventuring party all by himself. If you cross
  the line, you attract the paladin immediately.


Yes, it's true that these rules normally entail the Paladin joining the
adventuring party while they're still outside the dungeon, preparing for
their attack.  But crucially, there's no contradiction between the above rules and the Paladin joining mid-battle.  During battle the adventurer tiles are still in the spaces near the entrance, and it's easy for the Paladin to join them.  Just because in some sense the party have left the entrance and are now several tiles deep into the dungeon, doesn't mean that it's hard for the Paladin to find them.

Fundamentally, attracting the attention of the Paladin happens instantly at any point that a player becomes evil (or more evil) enough.  The rules are quite clear what happens whenever this occurs, and there's no reason to suppose there should be any exceptions.