He would not have been involved in the plot that cost his life...
The meetings and conversations he had about the military and political problem Germany had would still take place. The British are still going to be listening to wiretapped German generals conversions (taken in their POW estate for them) about what had been going on in France in the weeks and months prior and trying to piece everything together.
The comments they collected from the generals were too good for Churchill and the BBC not to use OTL during the war in part to demoralize German troops. And, from the BBC it went global to every WAllied newspaper via the AP I don't see them not making the same call.
Views on Rommel as a general were mostly based on what he did during the war among the WAllied public and armies before that point anyway. It makes for not quite as robust a post war movie with his house not being surrounded by SS troops and him not being being offered a deal he couldn't refuse by Hitler via SS generals.
But, by in large the course and historical views on him go the same way it did in our time line up to about the 90s. Views on him in the decades after the war had much more to do with what he did during the war then how he died.
Public views on him today probably face a somewhat steeper decline and they already had a steep decline as basically what the public knows today or at least those who do know about him is that he was a German general and how he died, but your average citizen of the Western world knew a lot more about the actual war not just in generalities thirty years ago.