Rules As Written, almost certainly not.
A grapple check is a special attack that does not use an attack roll. This means it probably doesn't trigger abilities that interact with "successful attack", per those rules.
It also absolutely does not trigger abilities that require an attack roll. You can't use War Gods blessing, for instance, to add +10 to a grapple check.
However, there is reason to rule otherwise as a DM
In particular, when an ability says "Successful attack", then the phrase "Special attack" in Grappling does suggest that it can trigger such abilities.
This does contradict Crawford, but Crawford's tweets are not RAW and non-binding. The DM has full authority to ignore them until they become PHB errata.
If you successfully touch an opponent as part of a "Special attack" than, in plain English, you are "hitting" them with an "attack". Despite not using the same rules terminology, there is clearly reason to interpret it that way.
What does this mean? How should you proceed?
I'd advocate looking at a particular ability and determining if it makes any sense to be triggered by grappling, then go from there.
In particular, the "RAW" answer means that Fire Shield, which wreaths the body in flames, does absolutely no damage if you are grappling them, but punching them with your fist suddenly does damage to you.
Given that this makes no sense, I am strongly inclined to support Rule Zero interpretations over anything the designers or unique legalistic terminology of the rules might say.
In order to have a logical rule-set, you'd need to re-write more text to turn grappling into a non-attack while preserving the intent of abilities that trigger off of hostile touches, than simply re-writing abilities that require attack rolls to make sense.