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Aquaplaning is always a problem, regardless of tyre compound, width, tread pattern, etc. Merely a matter of degree.
My insurer, Allianz, will not insure if I go wider than the placarded value. They were absolutely categorical about that, and fitting of other than OEM rims.
If one is going to do these things, one should get approval in writing from one's insurer. This usually takes the form of verbal assurance followed up by an amended policy document.
Aquaplaning is dependent on lots of factors, but two main ones are tread pattern, damp/wet road surface and how long since it has last rained heavily. It is caused by road grime molecules clinging to the road surface with their hydrophylic tails in the air, with water molecules hanging on to that tail.
A narrower tyre with a "better" tread pattern will be less likely to slide over those bound water molecules than will a wider tyre with a "worse" tread pattern. e.g. a good quality road tyre is more likely to cut through that layer of road grime + water molecules than will, say, an A/T tyre, or a bald one.
Regardless of tyre type and tread pattern, a narrower tyre will be more likely to cut through than a wider tyre. It's one reason that formula one cars switch from wide slicks to narrow treaded tyres if the rain starts to fall.
Simple physics and chemistry really.
