Depending on the model, it may work. You will need to get an app like PrintBot and try it out.
If your printer is hooked to a computer, you can install Chrome on the computer and set up Cloud Print to your Google account. Then get Cloud Print on your TF300 and link to your Google account.
Then you can print from anywhere with an internet connection so long as your computer is on.
Have you looked at PrinterShare? You can also use HPs ePrint service as an attachment. I have also used Cloud Print. I find the HP service to be the better, then Cloud Print. PrinterShare though is hit & miss at times.