Nope. You don't link accounts. You need to perform a standard bitcoin transaction and pay the fee, i.e. withdraw from CoinBase directly to Poloniex deposit address.

There's no minimum for bitcoin deposits (there are for some other altcoins, ie ethereum have min 1 ETH). But don't bother with anything in range of 0.001, the tx fee could be higher than that and it's a waste of time, I don't think you can place any order for such a low value, and you can't use lending option etc.

If you indeed have few BTC, just deposit more. If you want to test the site, make some trades, provide a loan, you'd need at least 0.01.