Yes - any parasite can. If your kitty has tapeworm, you'll often be able to see a segment on their butt - like a flat white thing - even just a small segment. Not seeing it doesn't mean they don't have tapeworm.
Best to get a fecal sample to Doc. It should be examined for parasites, period. Tapeworm and round worm are very common parasites. Unfortunately, over the counter products available at supermarkets and pet stores do NOT work. They simply cause the cat to expel the parasites. It does not kill the parasites or their eggs, and the cat becomes reinfested.
The only way to rid a kitty of internal parasites is to use a vet product (different, depending upon the parasite), and it will have to be administered in two stages - the first stage to kill the existing parasites. The second is generally after three weeks of finishing the first round. This allows for the lifecycle of the parasite - as the eggs mature, the second round of poison administration kills the next batch of adults. After another three weeks, a stool sample should be taken to the vet to make sure kitty is "all clear."
Some parasites have developed immunity to traditional treatment, thus the need to make sure the treatments worked. If not, you have to go another round with a different medication.
Our feral rescues had a parasite that was immune to traditional treatment, and it took us close to a year of trying various meds and combinations before we finally rid our pets of internal parasites.