Not if it is consolidated into a single transaction.  It can be a million BTC or 100 satoshis and it is still based on the number of transactions.  If you transfer .00001 BTC that is made up of 4 transactions, it would cost 4 times the fee of a million BTC with one transaction.  It is totally strange how it works - and that is why it is important to consolidate when the fees are low (and you do not care if it takes a few weeks to get merged together into one transaction).  There is nothing worse than having the market go crazy and needing to pay for something with more transaction fees than what you are trying to send due to lots of small mining transactions...