Provided you have a good starting location, yes, Deity can be beaten with any civ because the exploits you need to rely on in Deity work with Iroquois just as well as Poland: worker stealing, exploiting the DealAI, exploiting the AI's inability to use ranged soldiers properly, exploiting the fact that the AI doesn't choose optimal policy paths (Honor openers and ignoring Rationalism, for exampel), exploiting the fact that the AI doesn't choose optimal tech paths (so you can still beat it to key lategame techs), exploiting how hesitant non-Ghandi AIs are to use their nukes, etc. The problem is not that Deity is impossible to beat with any civ, it's that Deity is impossible to beat with any strategy that would ordinarily work in multiplayer (where the bad AI is restricted to CS's), so instead of being able to play around with policy trees like Liberty Settler into Reformation into complete Liberty into Rationalism, or Liberty Settler into Tradition, or even delaying Rationalism finisher thanks to Glory To God (you can purchase scientists without completing Rationalism, so you can put off completing it), and instead of being able to mess around with odd tech paths like Currency before Writing, you're forced to use the same, tired policy path (hard Tradition with a random opener into hard Rationalism) and the same, tired tech/build order (quick NC, ignore all pre-Medieval world wonders, etc.).