Yes and no.
Plenty of Jews have European paternity (in terms of Y-dna) because, from what I understand, Jews throughout history after scattering from Israel would sometimes have their daughters marry European men to form alliances in the local communities they'd settle in/near.
I'm unsure if the man would usually convert in this case, but the children of such a union would be considered Jewish and probably brought up Jewish in most cases at least.
What extensive analysis of yDna and mtDna among Jews has shown is that most of the yDna is Near Eastern in origin, while a lot of mtDna was picked up in Europe.
What has to factor into these analyses is that conversion was extremely rare in Europe between the days of the late Empire and the modern period because it was a crime under both Church Law and the laws of the state and was punishable by death.
Most of the "European admixture" which occurred in Jews is either very recent or took place before Christianity became the state religion during the late Empire. One exception might have been the incorporation of "gentile" women when the Jews fled far east and were welcomed there because some of the people were not yet Christianized.
As to the yDna, the vast majority is Near Eastern in origin. The vast majority of their E is NOT E-V13. The vast majority of their R1a is Z93, probably picked up in the Near East since it is the "Levite" yDna. The vast majority of their R1b is Z1203.
There is one small group of more western R1b. Whether one man converted, was circumcized and accepted into the Jewish community and somehow eluded detection by the authorities if it happened during the proscribed period is, I suppose, possible, but unlikely in my opinion. Perhaps it happened during the Roman period before the Empire became Christian. You'd have to know the precise subclade and age of that Jewish line, I suppose.
Or, some of these rare so called "European" lineages were the result of rape during the pogroms which went on through history. There's a reason why Orthodox women wear wigs to this day. In eastern Europe it became the custom for the women to shave their heads and wear head scarves to make them less attractive to rampaging Slavic men, or at least so I was told by a Jewish friend very learned in her people's history. I've always been rather surprised that there wasn't more of this kind of y. However, Jewish law, to the best of my understanding, permitted abortion until the child "quickened". So perhaps women did what they have often done rather than bear the child of a rapist.
Oh, and uniparentals don't determine whether you're "European" or African etc. There are R1b people living in Africa who are indistinguishable from their African neighbors. Are they "European" because of that yDna? I doubt it.