That is something that can be debated for a long while.
The basic gist of tech shirts is that they are supposed to wick away sweat the same way that certain types of running socks wick away sweat off of your feet. Y personal opinion is that it is a personal preference and if your not running long distances (say more than maybe 45 to an hour) unless you have a sweat metabolic rate (basically how easily you sweat) is something less to be desired than the answer is no. However, if you have a strong preference toward tech shirts or there is races you are prod of it wont necessarily hurt you either.
Any sweatshirt or t-shirt will do as long as you look decent. The reason is quite simply because in most cases there is not enough sweat to wick away. In most cases you can accomplish the same thing by simply wearing an undershirt. Most people who run will agree that if you are running in extremely cold weather than it is necessary to run in layers.
If you run in layers, then more than likely in sot cases wearing a tech shirt will defeat its purpose unless you are wearing it as the bottom layer. The reason for that is because you will not feel the whickering of the sweat and therefore it defeats its purpose.
Now onto the next question. What exactly are tech shirts? They are shirts made of cotton which has very specific type of flesh that looks like this. The main thing to pay attention to is the material of the shirt. The cotton has an extremely light feel, if any at all. If you do run long distances then they can be bought at most sporting goods stores and also at certain web sites such as REI for a reasonable price.