I'd agree. Pedantically, though, this wouldn't be GDP by definition.

I do think you can substitute "sum of numerical value" for GDP in most non-technical contexts and have them make sense.

In this case it could be that an economy doesn't trade 'rationally', so summing numerical values doesn't make sense. E.g. I'll trade you 1 chicken -> 2 shoes, someone else will trade 1 shoe -> 2 chickens.

I guess there would still be some numerical measure, but it'd be more of a matrix than a single number.