The mentos and coke thing is a reaction between the carbonation and the rough surface of the mentos. The water would dissolve the surface rather quickly, even in ideal scenarios, and as you melt the ice, you wouldn’t be able to re-expose the surface fast enough for a meaningful reaction. Just all around an impractical plan.
If I remember right from a video back when mentos and Coke was all the rage, it wasn’t just the texture of the mentos but there was also a chemical reaction in the combination of the two is what led to the violent reaction.
"The eruption is caused by a physical reaction, rather than any chemical reaction. " https://en.m.wikipedia.org/wiki/Soda_geyser
Would you be able to find the video? I had never heard of this, and can’t imagine what “chemical reaction” could occur beyond the carbon dioxide simply coming out of solution.
I can try, but that was probably 15ish years ago. So much has come and gone on the net since then.
I think it was mythbusters? It was something in diet drinks increases the effect over a regular soft drink.
For now, this is the best I think I can offer https://pubs.acs.org/doi/10.1021/acs.jchemed.6b00862#
Probably the sugar. Sugar decarbonates coke (and other sodas) pretty quickly. Add to that a container under pressure with only a small hole and you get an explosive reaction.