No they cannot be radioactively dated. This is because they consist of carbon and other isotopes that are being replenished actively. Hence, the standard level of their isotopes does not drop for us to calculate against the half life of a specific isotope.
Therefore, a specimen has to die resulting in the specimen being unable to replenish the isotope levels. Once the stores start decreasing actively we can easily find their age by radioactive dating. Of course, if part of the living specimen were to detach from the body and die, you could date the detached part as it is unable to replenish its stores of radioactive isotope.