it would depend on what kind of 'felt' you are talking about- not all 'felts' are created equal- craft felt (that you buy in squares in a craft department- is not washable- so, if you want your placemats to be washable it would not work well. wool felt is washable- but kind of expensive to use as a 'batting' instead of the 'main feature' (look up penny rugs to see wool felt placemats/projects)
there is felted cottons, fleece felt, many varieties.
what ever 'felt' you are considering you should first wash it & see what happens (unless of course you do not expect your 'placemats' to ever need laundering) then decide what is best.