This question intrigues me so, while I was just out for dinner with the wife and son, I thought I'd conduct a very scientific test with the help of some pictures (just the bass, no player) on my iPhone.
At the restaurant I showed 8 folks (no significance in the number) a picture of a Hofner Violin bass and then a picture of a Fender P bass. Also, if it's worth noting, 6 of the 8 said they liked music: I didn't go any further than that. I'd guess that everyone I asked was below 40 in age.
Ok, so for the Hofner not one person recognized the bass as a Hofner. 4 of the 8 guessed it was some sort of violin, 3 guessed it was some sort of guitar and one clever lady did identify it as a bass! When told it was a bass guitar and asked what famous musician would they associate with this bass no one answered Paul McCartney. In fact nobody had any idea, even when told that McCartney played one.
On to the Fender: 4 out of 8 identified it as a bass guitar, which was probably a bit easier having just seen a Hofner (I told you it was unscientific!). The other 4 identified it as a guitar and when asked what sort, said "bass". Of the 8, 2 identified it as a "Fender" another 4 said Fender when pressed for what type. When asked for a famous musician using a Fender, 7 out of 8 could not name one. The remaining person said "don't most folks use a Fender?"!
So what can you glean from my most scientific of experiments? Probably not much, apart from the fact that the folk I met tonight were into music but not into bass guitars! I think you could kinda get the impression that most members of the general public wouldn't know a Hofner when they see one and in general they don't associate any particular brands with musicians, well at least in Northern VA!
Science project over for the night. Now if only I'd had a picture handy of Gene's bass!
