Should a player get involved with their characters

It's not as lewd as you might try to make it sound. 

First of all I think in AD&D, or any other Role Playing Game for that matter, it requires a certain amount of "buy in" to make the game worth playing.  "Buy in" meaning suspension of disbelief and essentially pretending to be someone else.

For some people, it is little different than a board game.  A more literary version of chess and they handle their characters more like chess pieces or avatars than making any effort to "become" the character.

Then there are the "G.I. Joe" players who play as though they have an action figure in their hands and they are putting on a puppet show.

Moving on, we come to the "actor" perhaps what is most ideal in terms of role playing as they are becoming the character, at least in thought and "sitting at the table" playfulness.

We won't follow this to the next step because then I fear one is bordering on mental illness in believing they really are the character.

Now, none of these examples is "wrong" necessarily (except maybe the last one).  Some people are more comfortable with playacting and others are not.  They feel more "in control" of the situation by playing through avatars.

It's just a matter of the comfortability of each person.

Games seem to be the most fun when they have all or at least most of the players involved at about the same level.

Also, a lot of the "buy in" has to do with how involved the DM is and how much detail the characters put into the characters.

The fewer details applied to the characters, the less there is to "roleplay" the character as a unique personality. 

Some people are cautious about getting into the characters too much early on because characters die easy at lower levels.  Some people actually get so involved in their characters they become stressed "for real" when the characters "die" in the games.  Thus, they intentionally play the characters as avatars until the characters survive to a more survivable level and begin to fill in the personality and details.

Going back to the DM's role in this.  A charismatic and very engaging person who is a good story teller and narrator can make the players feel a lot more comfortable about "getting into character" during the game.

Having said that, they can go a little overboard and take over the story, not leaving much room for creative stretching of the Player Characters as I mentioned in the last post.  It's a balancing act for the Game Manager.

However you approach playing your characters though, make sure you do so in a way that is comfortable to you.  Playing a game, especially a role playing game, is no fun at all if you aren't able to relax and have fun.  If you are feeling stressed and uncomfortable about the game, you won't have fun and it will most likely impact the environment of the game for everyone else too.

This is something to consider for the other players at the table who are more comfortable with role playing and "getting into character".  Don't push other players too hard, mock, deride or chastise them for not getting into things as much as others at the table.

After a few times they'll either get more comfortable and get more involved on their own or they'll decide that it's just not the kind of fun they really enjoy and move on.