Short answer: No. Your order gets routed to the fatstest and most profitable platform for your broker, not you.

Long answer..........

Alpha is an Alternat Trading System (ATS):

During the week ended May 13, 2011, Canada's top three alternative trading systems captured 31.6 per cent of trading volume. Alpha Trading Systems came first, trading an average of 223 million shares a day, or 22.1 per cent of volume. Chi-X Canada came second, trading 58.2 million shares a day, or 5.7 per cent, and Pure Trading came last, trading 36.8 million shares a day, or 3.6 per cent. Together, the Toronto Stock Exchange and the TSX Venture Exchange were left with 67 per cent.

Of securities listed only on the TSX, Alpha captured 23.2 per cent of trading, Chi-X captured 9 per cent and Pure took 5.7 per cent. The TSX was left with 59.6 per cent. Source: here

Alpha is owned by the Big Canadian Banks and they will route orders through there in order to pay themselves as opposed to paying Excahnge Fees (ECN Fees) to the TMX. In the US there are far more ATSs than in Canada and there are far more "dark pools" which provide liquidity. We are relatively primitive here. More on dark pools here

The only alternative listing in Canada besides the TSX/TSXV is Pure that operates the CNSX.... but who has ever traded a stock on the CNSX or even has access to it?

Interestingly, the same group that owns Alpha is put toghether the counter offer for the TMX today.