Vaccines greatly reduce the risk of infection. That said, they don’t fully protect you, and given the variants in circulation right now, there is a high risk for someone who has just been partially vaccinated.
After full vaccination, when immunity is said to reach its peak, the risk of infection and the results are well minimized. From a low risk of hospitalization to serious illness, vaccination can save you many ill effects. However, there is a great risk of contracting the infection, it is possible that some symptoms will develop, and therefore, in theory, it is also absolutely possible to develop a prolonged COVID.
However, there is no evidence-backed data yet to determine the risks and possibilities.
Despite this, scientists remain hopeful that COVID vaccines, like other vaccines, may work to reduce the likelihood, duration of symptoms, and long-term complications. How well it works is something in practice, we will only learn in the next few months.