If I use my pool or a site like bitrex as a wallet and I "withdraw" my payment to buy machines from bitmain/canaan will this cause any kind of issues?
I think you want to buy a product of bitmain with your bittrex balance(btc/ltc), isn't? AFAIK you can do that, but you should consider the withdrawal fee from bittrex, it's 0.001 in btc.
Note: I wouldn't recommend you to use exchange as wallet, use a wallet which you can control the private key. And if there are any trouble with your payment, it's hard to get back or may even be your coin in limbo.
