Yes, the Visogoths had conquered Roman Hispania.
However, the Visigothic Kingdom was comprised of a small barbarian warrior class that ruled over a vastly greater Hispano-Roman population that had been an integral part of Roman civilization since 200 years before the birth of Christ.
The civilization of Hispania that produced Hadrian, Trajan, Lucan and the aqueduct of Segovia did not need Muslim invaders to "civilize" them.
The miniscule effect that the Visigothic invasions had on the culture of Hispania is evident by the fact that, today, the Visigothic Germanic language is totally extinct in Spain except for a few lingustic peculiarities in Castilian. Except for the Basques that speak their pre-Roman language, every other region of Spain today speaks a Romance language that is a direct descendent of the Latin language of Roman Hispania.
Aquaduct of Segovia. Circa late First Century A.D.
Denarius of Hadrian honoring Hispania. Circa 118 A.D.