It is very plausible that Joe will get caught.
US currency uses a paper made of a blend of 75% cotton and 25% linen with added red and blue synthetic fibers (see this PDF for more information on security features of the $100 bill, such as an embedded thread that glows pink in UV light). This blend of paper will feel different from standard home/office printer papers, which are made from wood pulp. Furthermore, US currency uses the intaglio printing process, which results in slightly raised ink on the surface of the paper. This process also causes the paper to be slightly thinner, due to the pressure used to press the ink into the paper. The raised ink also affects the feel of the paper. Bank tellers are trained to recognize counterfeits by feel, so Joe would need a source of rag paper and hope that his mystery printer can mimic the results of the intaglio printing process. Otherwise he would quickly be found out.
Using existing serial numbers actually doesn't seem to be a problem unless the person handling the money has two bills with the same serial number in hand. In fact, not using existing serial numbers would likely mean the serial number is out of the range used for $100 bills. And while the clerk at a store where people are likely to buy over one hundred dollars worth of goods might not recognize that the serial number isn't legitimate, the teller at a bank will likely know the range.
As others have pointed out, it is how Joe spends the money that will be the biggest cause of whether he gets caught or not. The more he uses his counterfeits, the greater the chance that someone will recognize them as counterfeit. If he tries to pass the bills off to family, friends, or coworkers, they may very well remember that it was Joe who loaned or gave them the bad bill if it is discovered as counterfeit.
In fact, Joe would be less likely to be caught if he counterfeited $1 bills as there are not as many security features to deal with. Granted, Joe would make considerably less (and depending on the cost of materials may end up losing money), but he would also have other benefits. Lower denomination bills are scrutinized less, which means a greater chance of successfully passing off the bills. There are more places to spend lower denomination bills without raising suspicions, which gives Joe more avenues for passing the bills. And making less money through the counterfeiting operation would reduce the temptation to splurge and, thus, lowers the risk that Joe's spending habits reveal his operation.