Here's a VERY scientific link that describes what you're asking....
http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1005&context=textiles_facpub
To narrow it down, no, not in any measurable terms will flourescent lighting fade your "felt" within a negotiable timeframe.
Felt is a non-woven cloth that becomes solid by pressing stuff together.
Using
UV lights will sap the dyes in weaved wool cloth, which is what decent table coverings are made of. But, we're not using UV lights, and hopefully not felt.
Bottom line simple answer to your question......"No sir it won't"