It all revolves back to whether it was a "single strike", and to what extent the demand for Japanese "unconditional" surrender was justified. Both come with more than a whiff of "what-if" to make sense — a number of pretty big assumptions are required, and that's regardless of bombs or no bombs, and terms or no terms.
Since the bombs didn't appear as single strikes out out the blue, but were preceeded by a year or so of very considerable US bombings of Japanese populations centres, the sad fact was also that Hiroshima and Nagasaki had at least partly been relatively spared so as to have someplace to nuke. US conventional bombing could have flattened them just as well. AND the Japanese were on their last legs already, and knew it. So what remains is the possible argument that the nukes were a sign the US could still amp things up considerably, and that — specifically — settled the matter. The problem is still that it's by necessity an unknown if the same outcome might not have materialised even if the US hadn't had the Bomb? It's just not possible to know for certain.
Put another way, the problem also is IF the US has accepted some minor negotiated modification to terms for Japan, that would allow the Japanese imperial family to stay on the throne — possibly nerfed to be mere constitional figureheads on US insistance — would that have been so terrible, if it ended the war before an invasion? The answer, like quite often is, is probably that it all depends on what the US would have done NEXT, to "win the peace" in Japan. Considering the US in the end had not just the imperial family remain, but the actual emperor (whom I think they could well have demanded should step down in favour of someone less implicated), at least nothing indicates allowing Japan to name perhaps a single condition for its surrender is unlikely to have cause any lasting bad effects. No nukes, and the US being reasonable like that in the post-war era in Japan might as well have been seen as a case of US non-vindictive fair-mindedness, and an asset — rather than some kind of weakness for a militarist Japan to stage a resurgence from (if that's the worry).
I.e. there are a bunch of factors that might still have decided it all in such a fashion that the Japanese main islands wouldn't have had to be invaded, the nukes not dropped, and post-war Japan still turning out as it did historically. Oh, except possibly minus the Ginormous "National Nuke-Victim"-complex post-war Japan developed.
One might even wax ambitiously hypothetical here, and ask whether without the nukes it might even have been possible that Japan would have had some kind of post-war responsibility debate more akin to what the Germans had about their role in the war, better and more comprehensive? It's a long-shot certainly, but without the Japanese collectivised, vicarious experience of being "the only country nuked in WWII", at least it seem more than likely it would change the tenor of a Japanese post-war self-understanding.
Just supplying a bit of detail... 
