It would use both. You have to have internet access to utilize the handcent application, and in order to receive text or send text messages it would pull from your account features. The application just enhances your options while you are texting, such as customizing and different styles of texting.
These are my favorite apps
Flixster = movies times and previews
Estrongs File Explorer = I find it more user friendly than Astro
Speedtest.net app = test the speed of signal!
Colornote = Little post-it notes that you can edit and assign different colors for task, lists
Swiftkey Beta = Keyboard replacement. It's not Swype but I like the learning aspect of it and feels quicker than the stock keyboard of my Eris
The Weather Channel = I don't even use the weather widgets that came stock any more because having this.
Sensorly Map viewer = crowd sourced cell signal maps from around the world and growing everyday.
Here are my tops apps on my Droid Incredible:
3 Music Player - Let's you view your album art in a cube and works with all integrated playlists. Has different orientations available and I enjoy it over the default music players.
App Protector Plus - Lets you put apps behind a pattern or numerical lock. Very ideal for wanting to show off your phone but not wanting to open some *ahem* questionable apps.
Beautiful Widgets - Best home screen clock I've paid for. Makes HTC Sense tolerable. Then again I've had a Droid X with 2.1 and that was a complete nightmare, so this just enhances the Incredible for me.
Blow Up - Wasted hours playing this addicting game.
CardioTrainers - Tracks a majority of my workouts and integrates my music playlists. Voice announcer lets you hear how much you've accomplished. Very motivating.
jetVD - Best You Tube ripper out on the market. I had TubeDroid which worked flawlessly. Then one day it disappeared from the market and never worked, Sirius never responded to my e-mails.
Movies App - Lets you stream Netflix, view movie previews, read reviews - perfect movie app.
MyBackupPro - This app backs up the actual app and the market link. Backs up your phone settings. It was my saviour once I got rid of my horrible Droid X.
Photofunia - Let's you use your Gallery or take a new pic and insert into scenic or funny situations. Let's you share via MMS or Facebook/Twitter/etc.
Safe Neighborhood - Let's you view sex offenders in your area.
Soundhound - Sort of like V Cast Song ID except you could hum the tune and it usually gets it right. Doesn't have a lot of Clash music though for some strange reason.
SpecTrek - Got my lazy niece and nephew outside to walk. Uses your camera and GPS to hunt ghosts in your area. Check it out.
Video Ringtone - Ringtones are outdated, now play your favorite music video via your sdcard. Or you can download over 100 options the developer has. Works flawlessly now after some major needed updates.
Wow! That is a list! A few of those I use as well, but I think I will give some the others a try after the holidays.
This what happens when you have a habit of testing app and looking for things better and greater, some times you find a list of favorites. And the scary part is I use almost all of the apps listed daily..