Why the question mark? Because I believe that the political outlook of Sinn Féin is at best ambiguous. A left-wing political stance co-exists with other elements and we cannot be certain about how the party will evolve in the future. Perhaps I should start by making my own position clear; if Sinn Féin could be part of a putative Progressive Block that could displace the dominant duopoly of Fianna Fáil and Fine Gael in the political system of this Republic, I would be optimistic about the success of such a political project. In other words if Sinn Féin, as it operates in this jurisdiction, could become part of a broad left that could credibly bid for power, I would be happy. But in considering this possibility we need to combine optimism with scepticism. 
In the totality of its outlook and activities Sinn Féin is, fundamentally, a nationalist political movement. It may well, for a host of tactical and strategic reasons, want to position itself as a left-wing nationalist party. Sympathetic academic commentators like Dr John Doyle of DCU would explicitly reject the fact that Sinn Fein is an "ethnic nationalist" party and would instead seek to link the party's nationalism with anti-colonial struggles and the anti-globalisation movement (see this previous post). This is not a stance the party is likely to emphasise when on fund raising jaunts to the US. While the party as it operates in the Republic is locked into a an ideological stance that is undoubtedly left-wing, at other times and places Sinn Féin will want to be seen as more centrist and accommodating. This is especially so in the kind of consociational democracy of the type Northern Ireland is set to become.
Fundamentally, being a nationalist party means that Sinn Féin will refuse to accept that there could be an irreconcilable clash of interests where the party would have to choose one mutually antagonistic interest over another. I raise this issue as a belated response to a very interesting post over at the Cedar Lounge Revolution. Furthermore I also raise this in the context of a 'progressive' block emerging as a left force after the next general election. The nationalist character of the party makes me a little sceptical about whether Sinn Féin will form part of this block.
This is apart from the rather separatist caste of mind of the of the party in terms of its broad political culture - the 'ourselves alone' element of Sinn Féin, as it were. Apart from involvement in the peculiar institutions of the Belfast Agreement, the party has shown few inclinations to enter into co-operation and dialogue with other political forces. On the other hand there are some grounds for optimism that Sinn Féin can eventually emerge as a more normalised political party. As everyone knows Sinn Féin was a subordinate element of a tightly controlled military movement. That kind of centralised command and control structure is not so easy to operate once the party operates in a more open political system. A comparison with the Workers' Party is instructive here; its democratic centralist, Leninist discipline broke down under the impact of electoral success and having to operate as a 'normal' parliamentary party.
Then there is the argument that if it thinks it ought to quack like a duck and generally take on the appearance of a duck, then it perforce behaves like a duck. Sinn Féin, in the Republic at any rate, may well become locked into a rhetoric of left politics where its leaders and activists are increasingly likely to justify their stances within the norms of a broadly left wing ideological and strategic framework. This is why it's important to start thinking about how to give this as yet notional progressive block some substance after the next election, regardless of who is in government, and not waste time on which existing party can lead it or not.