Thanks for your answer @DannyHamilton. And you are right, my description is rather confusing. So let me express it with an example:
For a given tx the amount to be sent is X btc. The (suggested) tx fee for this tx is Y. However, X = Y, so there's no point in sending out this tx. So my question is, does the above occur for any given value of X?
My arbitrary assumption is also that amounts smaller than X will need more fees to be sent than the actual value, I might be wrong on this one.
The suggested fee is based on the size of the transaction (in bytes), not quantity of bitcoins being exchanged.
The suggested transaction fee is currently suggested in increments of 0.0001 BTC (100 µBTC) per kilobyte.
So, a transaction that is sending 0.001 BTC (1,000 µBTC) could have a suggested fee of as little as 0.0001 BTC (100 µBTC) but if the transaction consisted of many inputs and many outputs, the suggested fee could be higher than 0.001 BTC (1,000 µBTC).
If we assume the smallest possible transaction (only one input, and only one output), then you are looking at a transaction that is less than 1 kilobyte. Therefore, the smallest possible transaction fee (on a transaction that has a transaction fee) is 0.0001 BTC (100 µBTC).
Based on your quote above, this means
Y=0.0001 BTC (100 µBTC).
If
X is less than 0.0001 BTC (100 µBTC), then the fee is more than
X.
If
X is more than 0.0001 BTC (100 µBTC), then the fee is less than
X.
Of course, depending on the contents of your wallet, it is possible that the transaction is not less than 1 kilobyte.
This means that
Y may increase even if
X stays the same.
It depends entirely on the quantity and values of the unspent outputs in the wallet and the number of new outputs your transaction is creating.