Hi,
To my understanding, yes. There is a delay while the MOSFET capacitance is charged until the device turns on (gets enough energy to make electrons and holes start to bounce around and cross over the (band)gap, so to speak) and then also the time for the output to go from e.g. '0' to '1' or '1' to '0', like charging or discharging another capacitor.
Another loose, inaccurate, but hopefully comprehensible way, of seeing it: Gate is one RC network, Source-Drain is the other RC network.
Have a search for MOSFET gate drive and such like, many documents will explain it in more or less complicated way depending on if written at component user level or transistor designer level.