Can free bitcoins from faucets be actually spent?
You could consider creating a new address with 0.01 BTC on it, then sending the concatenated amount at 0 trx fee to each of the addresses containing the smaller amounts.

So: 


0.01 -> first address 
First address (now including the 0.01) -> second address
second address (now including the 0.01+first address -> third address


... ad nauseum.