The answer is yes. The fallopian tube is a mobile organ responsible for collecting the oocyte once it has ovulated. It is also the site where fertilization takes place (sperm and egg usually meet in the ampullary portion), the duct that connects this site with the uterus and, therefore, with the outside of the woman. The fallopian tubes also have the important function of serving as an incubator for the development of the already fertilized embryos, moving them carefully by means of their cilia to the uterus, in a journey that will last approximately 5 days.
All these functions are performed independently by the two fallopian tubes. Thus, when one of them is missing, this cadence does not affect the other one, which could even pick up oocytes from the contralateral ovary. Therefore, even when one tube is missing, the patient can become pregnant.