I actually teach my catchers to talk to the umpire and batters. Especially the umpire. The catcher should know the umpire's first name before the game starts (I always write the umpire's first names on the line up card so the kids know them). By having small talk with the umpire and calling him by his first name, you can develop a rapport with them. As for the batter's, I don't think a little small talk is bad. You definitely don't want to talk trash back there, but a little small talk during the at bat wouldn't hurt.
With that, I give you the story of my first (and last) professional at bat....
As a relief pitcher in a National League organization (where pitchers only hit in Double A and higher), I didn't do much hitting. In fact, it had been about 8 years since I had hit in a live game (since high school). We were getting blown out and the pitcher on the mound for them was a LHP Prospect throwing 99mph. He was throwing a no hitter that day. When I came in from pitching my inning, I threw my jacket on and stood by the heater (it was freezing that day). Then I heard someone say "Madden, you're on deck". I said "WHAT????". I thought they were joking but then I caught eyes with the manager and without a word I knew it was no joke. So I said "Does anyone have a bat I can borrow". One of my teammates reluctantly handed me his bat and said "please don't break it". The batter ahead of me just struck out so as I was running out of the dugout I grabbed the first helmet I saw. It was way too small. But, it was too late, I was in the box already.
With my helmet sitting high on my head, I dig into the batter's box with no warm up swings. (Here's where this story relates to this thread). The catcher says to me "what the hell are you doing up here?" in which I replied "they sent me in to break up this no hitter". Them umpire and catcher started laughing as the first pitch came in. A 99 mph fastball in the dirt. I'm not sure what I said or what my reaction was, but the umpire and catcher were hysterically laughing. The catcher then asked me "are you going to swing at this next one?" in which I replied "I'm just going to try to keep my eyes open for this one". They continue their laughter. 98 mph fastball for a strike on the outside corner. 1-1 count. I've got him right where I want him! At this time, the announcer realized who was hitting and changed the picture on the big score board to a picture of me and announced me over the load speaker. I say "Oh man, look at that guy" reffering to the picture of me on the big screen. "I just can't wait for tomorrow". 98 mph strike on the inside corner. The catcher says, "why, what's tomorrow?". I says "cause I get better looking everyday". Umpire and Catcher crack up again. I get in to my 2 strike approach. The catcher says "ok, here comes another fastball". I had already decided to swing at anything that was remotely close but I couldn't tell if the catcher was serious or not. 99 mph Strike 3, way outside but right to where the catcher was set up. So, I think that because of the small talk he got me second guessing myself for a split second on the last pitch and he had a rapport with the umpire which I think helped in getting that outside pitch called for a strike. Not to mention it was 30 degrees and everyone was ready to get out of there.