Would there be any noticeable difference (or any) if one was to use fiber cables for their LAN even if there was a standard copper connection coming into the network?
Not on a "human scale". Copper interfaces tend to be microscopically faster (nanosecond scale) because the signal is already electrical. An optical interface, however, has to go through additional logic to make it electrical.
(I've heard of pure optical switching, but that was only a lab experiment.)
Depends on the LAN.
In mine, there is a huge, noticeable difference, because the LAN extends across multiple buildings scattered over 1/2 mile, and served by different power lines. When it was copper it did not cover as many buildings, because copper would not reach, and burnt out ports were a common result of thunderstorms.
With fiber, thunderstorms cause no problems to the network at all, and even on the wimpiest (singlemode) SFPs link length is 10 kilometers, so nothing anywhere on campus is out of reach, no matter how convoluted the run.
If your LAN is not hampered by 100 meter length limits and is within one building, there will be virtually no noticeable difference.