The market structure does not matter; the strike/price/numbers that you input and output are going to be what matters. Write out everything you plan to do, the prices, the fees, etc. and see if you come out positive, or if you're daring and confident you can just go for it and make the trades/purchases and see if you end up with more money. Either way, you will have your answer, but without more information, criteria and parameters there is no way to respond to your question, except with more questions.
For example, though - if you took BTC/USD on bitmex (which doesn't support USD deposits/withdrawals, instead uses a price pegging system), and BTC/USD on bitfinex, which uses USDT, arbitrage is not possible, because there's no way to exchange USD between exchanges, so market structure does matter in this case.
I'm just wondering what the constraints are? Is it simply the ability to deposit/withdraw the base/quote currencies on both exchanges?