I think Kerry was an extraordinary Secretary of State, who did those two things that I think no other Secretary in his place would have been successful.
However, as President, he might likewise have beaten the odds to do things better than could have been hoped for. He clearly would have managed a better exit to Iraq - given either his stated plan at NYU in 2004 or the later Kerry/Feingold for that matter. That could have avoided the Sunnis on the Iraq/Syria border being so powerless that they became ISIS. Kerry, even in 2004, was speaking of working with regional powers to get an inclusive government.
I also think that the very active Kerry would have - as he said - worked very hard and been very involved in fixing the areas damaged by Katrina and connecting that problem to the environmental issues, both local and climate change, that made that disaster as bad as it was.
Also back to the 2 big SoS accomplishments:
On Iran, I first thought that the timing would have been wrong because there would be no one like Rouhani in Iran. However, The President of Iran in 2005 was the pro democracy Khatami. He was in office until August 2005. I would assume that a President Kerry would - as he said in the foreign policy debate - have joined Europe in negotiating with Iran. (Maybe he would already have made his friend and adviser Moniz, Secretary of Energy.) In this case, the President would himself have been 100% behind the effort.
On climate change, I remember that he was, as the only Senator to go to Bali, instrumental in the agreement they reached --and he was even thanked in a SFRC by the Bush people for his work there. Ban Ki Moon spoke of the Paris Accord deal having its roots in the Bali agreement. This was reported as crediting the Bush administration, but what was not noted was that Kerry was key to the US/China pact and Paris ... and was important to the Bali conference, not through position, but through competence. Remembering that, I agree that with Kerry as President, Bali would not have been a last minute scramble to get something, but would have been something Kerry himself devoted time, energy and leadership on.
So, both of these efforts could have happened earlier -- and just as happened under Obama, they would have had to be done in a way not needing to be treaties!
One bonus, I remember in 2005, Kerry speaking of how the death of Arafat and Abbas becoming the Palestinian leader was a window of opportunity. Where the Bush administration pushed Israel to insure that the Gaza elections happened on time, Kerry thought they should be delayed as many in Israel wanted fearing that Hamas would win with the PA in chaos. Kerry cited Abbass as telling him that he needed resources to provide government services to win approval of Palestinians. Given history, peace in Israel would not have been easy or anything but a longshot ... but a better chance than in 2013!