We actually add the customer information in the installers, making each installer unique. The reason is to make it easier for the users, not to track pirated copies.
I would not recommend it though.
For us the choice was between having to several different installers, do some advanced scripting that alwasy would work on all OS combinations or to come up with a way to patch the included software (it took a while to get the vendors to agree to this).
The drawback is that you will have to build each installation from scratch or that you can't use most of the installers. We have found one installer that with a bit of tweaking allowed us to patch things into the exe-file while customer is downloading the file from our web server.
I would focus on making a good product and making the product as easy as possible for the users that want to pay for the it. Many users that would use a pirated copy wouldn't have bought your software anyway, they would just have used some other software. Isn't it better that they use yours? Some time in the future they might turn into a paying customer.
I'm not advocating to use pirated software. I'm just saying that a startup shouldn't worry to much about it. If it turns out to be a problem and that it is affecting the sales (i.e. it is easier to use a pirated version then to pay and use the real version) it is time to do something about it (probably to make it easier to buy and install the real version).
The information about which copy that has been pirated is probably useless. Most customers are very loyal and don't leak copies to warez web sites intentionally. It is a lot more likely that someone copied the software without their knowledge.