Influence of incident signal on antenna S-parameters
A signal being received by an antenna has no effect on the S11 of the antenna, but it might have an effect on the measurement of the S11 (depending on what the signal is).

The way you measure S11 is to throw an electrical signal at the antenna terminals (geneally written \$a\$), and measure the signal coming back (\$b\$). The S11 is then calculated as the ratio of reflected to transmitted, \$S11=\frac{a}{b}\$.

If you try to measure the S11 while an RF signal is incident on the antenna, then the measured signal will comprise the linear addition of both the \$b\$ reflected from the antenna, and the incoming signal. 

If the incoming RF is uncorrelated with the \$a\$ signal, then the result will be a noisy disturbance to the S11 measurement, which can be averaged out as noise.

If OTOH, the incoming RF is a reflection of RF actually transmitted by the antenna as a result of the \$a\$ signal, then it is correlated, cannot be averaged out, and is in some sense a true measure of the S11 of the complete antenna assembly, as you have it set up to be measured. For instance, consider a reflector antenna with a feedhorn, if there is some structural support reflecting signal inadvertently, that is still part of the overall antenna's S11.