No, they aren't powerful enough.

First, nukes are nowhere near as powerful as a comet impact. A large comet would release about as much energy as 625,000 of the Tsar Bomba, at fifty megatons, the most powerful nuclear weapon ever tested.

A single large comet impact is equivalent in yield to around 625,000 of these - the most powerful nuclear weapon ever tested

Then, comet impacts also are not powerful enough either, as they haven't terraformed Mars yet.

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Comet impacts haven't terraformed Mars

It is true that Mars can be pushed into a runaway greenhouse effect, where all the dry ice gets evaporated into the atmosphere.

However, to get to that point you need to have an atmosphere that is about 10% of the atmospheric pressure of the Earth at sea level. Mars current atmosphere is 1% so you need to somehow release nine times the current amount of CO2 in its atmosphere.

From this graph, Chris McKay, a leading planetary astrogeophysicist, deduces that to get Mars to go into a runaway greenhouse effect using just CO2, it needs about 100 millibars - or same pressure as 10% of Earth's atmosphere, to be released into the atmosphere.

It is not clear whether Mars has that much dry ice. There is enough to double its atmosphere. But to end up with ten times its current atmosphere is less certain.

If you don't release enough CO2, then it will revert to its current state because a denser atmosphere would be out of equilibrium with the vapour pressure of the dry ice at its poles, so it would all condense back to its poles as dry ice.

The amount of CO2 released by a single Tsar Bomba is tiny, even if you dropped it directly on a known dry ice deposit at the poles. You would need billions of them to release enough to push it into a runaway greenhouse state.

For more of this see my Why Nukes Can't Terraform Mars - Pack Less Punch Than A Comet Collision

(This answer is a taken from the summary introduction to that article,. just copy and paste, which I can do as I'm the author of the article)

Elon Musk later clarified it by saying that he meant nuclear weapons detonating continuously over both poles of Mars to create two new mini suns - a far future sci. fi. scenario.

"What I was talking about," said Musk, "was having a series of very large, by our standards, but very small by calamity standards--essentially having two tiny pulsing suns over the poles.”

Elon Musk Clarifies His Suggestion To Terraform Mars By Nuking It