Arduino is running as a server, but want to occasionally act as a client to update time
There is no problem with running multiple servers and use multiple clients with the WiFi library of the ESP32 core for Arduino as it is not a problem with most of the WiFi libraries for Arduino (some can't run servers (TinyGsm) or can run only one server (WiFiEsp(AT)).

But you don't need a WiFiClient for NTP time. First because NTP runs on UDP and second because the ESP32 SDK provides SNTP and the ESP32 core for Arduino wraps it in functions presented in the ESP32 examples library's SimpleTime example.