Rooting in itself, won't necessarily, but things like installing custom ROMS after unlocking the bootloader and rooting can/will, I have CM10 UNOFFICIAL on my device which runs Android 4.1.2 and that alone on the HTC One V is SOOOO much smoother and faster than the stock 4.0.3 with Sense 4.0 on the HTC One V.
Also when installing custom ROM's you flash boot images which contain kernals to allow overclocking and speeding the phone up, tho it can drain the battery, I can run mine at a stable 1.7 with no reboot's or problems.
It's not all that hard to install ROM's or boot images once you have followed the guide on this site to unlock your device and flashed a custom recovery image.
How to unlock, flash, root, backup your phone to be able to install ROMS:
[GUIDE] How to Root the HTC One V
The ROM I use, both links for CDMA/GSM:
The newest CWM Recovery for CDMA/GSM:
GSM - http://forum.xda-developers.com/showthread.php?t=1871243
CDMA - http://forum.xda-developers.com/showthread.php?t=1942749
Boot Image/Kernals for CDMA/GSM:
Goo.im Downloads - Downloading JellyBoot5.zip
Titanium Kiss - http://forum.xda-developers.com/showthread.php?t=1765687
Titanium Kernal - http://forum.xda-developers.com/showthread.php?t=1765687
Also, here is how to install the original RUU, should you accidentally brick your device:
[GUIDE] Re-flash stock ROM (RUU) after bricking a rooted device
If you do not see your RUU there, you can PM football on XDA and ask him to get yours, but sometimes he charges to find them, I had to pay him to find mine, but it was worth it just in case.
Now there are tons of custom ROM's made by the community, but CM10/AOKP are the two main popular ones.