I believe the impact was nearly to none, Modern iberians are pretty much Celt + Native Iberian and the rest made of Germanic and MENA, there very few cities with roman occupation, the domination was cultural, not genetic, its prty much like finnish ppl, who are like 5% Siberian but speak a Uralic language, in my opnion (Based on g25 samples and IllustrativeDNA) a avr Iberian is +/- 45% Celt 35% Pre-Celt Iberian 15% MENA (Mostly NA and Levantine) and the rest is Germanic and Roman.
In mostly g25 i dont even score Italian, in IllustrativeDNA my european side is only Iberian, C. Celt and a little of Sarmatian (Misread PIE maybe?) and my fit generally is ~1, i barely see any Iberian scoring real Italian, when someone score roman or etruscan in 99% of the case its just misread Iberian/Tartesso\Lusitan bcs they are similar in genetic terms, and some Iberians just score N. Italian bcs they are just similar components, The major diference of N. Italians and Iberians are just bcs N. italians have more Anatolia\Levantine like dna and Iberians have more N. African like, if u are a iberian-descendant but more levantine shifted\Admixed (Like me) u prob will score a lot of N. Italian, its just Misread.
IllustrativeDna:
41.2% West African
20.6% Iberian
16.2% C. Celt
9.6% Phoenican
3.0% Egyptian
3.0% Bantu
3.0% S. American
1.6% NW African
1.0% Pygmy
0.8% Khoisan
Fit: 1.095
I just take off Zagrosian\Sogdian\Sarmatian samples bcs my CHG (Part of my yamnaya ancestry) was begin misread, and i dont have any Iranian related ancestry and looks like Jews dont score this too so this dont rly makes sense and the distance are prty much the same (Go from 1.078 to 1.095) so i guess was just misread CHG and ANE