Yes and no, but it depends on which tent you have.
Our TREK tents have an outer fabric of polyester, with polyurethane coating (PU) on the inside and impregnation on the outside. The impregnation on the outside will wear away during use, and you can nicely re-impregnate if needed. Such impregnation intended for synthetic fabrics without a membrane can be bought at most sports shops. Some such impregnations will also help protect the tent fabric from the polyester tent's perhaps worst enemy, UV rays.
Our PRO and X-TREM tents are made of silicone-treated nylon. You can not impregnate such substances, as the impregnation will only bounce off the silicone. But this is not a problem either, as silicone-treated nylon can not be affected by wear and UV radiation in the same way as PU-treated polyester, and the tent will stay waterproof for many years, without having to be re-impregnated.