Is it reasonable that a problem "solved" by a traditional ANN can also be solved by a CNN? There is a data science numerical problem, which me and my team were able to get an ANN model that predicts down to a 1% MAPE error (with roughly 70000+ trainable parameters).

Given the nature of the dataset, this data can also be processed as images, which has led me to trying a CNN based approach to solve the same. As of now, I'm able to converge to error figures of 14% with around 2000 parameters. Is it reasonable to assume that I'd be able to bring down the error even further with a CNN based architecture (without a significant increase in the parameters)?

EDIT: Basically, what I mean by image is, in the ANN case, the data is being processed as a 1D vector, but as a 2D vector in the CNN case.
In theory yes in practice maybe.

What do I mean by that. There is universal approximation theorem for smooth functions regarding ANN, there is also theory backing this up for CNN variant. Another thing that backs this claim up is that you can replicate any ANN with CNN architecture, hence effectively backtracking to the original ANN.

Practice, you say this data can also be processed as images it can be processed but does it have the same amount of informativness as other data representation? Could be but it does not have to, think about doing regression with images of time series data, sure you can catch some general trends but to really catch all of it it will get expensive, really fast.