No, they couldn't have. Canon makes nice stuff but they're nowhere near where ASML is.
It is however possible that Canon will at some point in the future be able to compete with ASML for all of its line-up, but Canon will have to make up for at least a decade of lag and for the industry that means that they're not relevant for the cutting edge. The amount of investment that they would need to make to be a serious threat to ASML is something they do not currently have in the works.
Industry watchers are skeptical about Canon's 'NIL' product, there are serious concerns about flaws in the process resulting in low yields. Maybe they'll be able to iron those out and then they may well become a contender. But it's an entirely different path than the one that ASML took and as those bets come a bit of a risky one (but with correspondingly high pay out if they get it to work). For now ASML is 90% of the market or so...