I doubt it, I've never heard of them and we get more American telly.
The Bowery Boys series were movies, not a TV series. They were fictional New York City characters who were the subject of 48 (yes!) films released from 1946 to 1958. I have a feeling that they probably didn't travel well. The humour was sort of Three Stooges/Abbott & Costello type. Actually reading plot resumes they sound like a lot of fun.
Yes. They mimicked the early 20th century New Yorkese, when New York's five boroughs had a larger working class demographic of white, blue-collar types. I don't remember if they spoke with the classic early 20th century New Yorkese, or perhaps, Brooklynese, "dees, dem and dose" ("these, them and those" - the Irish didn't pronouce "th's," as I've read was the origin of that speech), they seemed quite comfortable with their speech. The comical effect was Mugs McGuinnes, I think (I forgot the actor's name) who was known as Mr. Malaprop by the media, since he used five dollar words incorrectly.
Many younger New Yorkers have interestingly lost any New Yorkese, other than pronouncing New Yawk, instead of New York, or "idear," instead of "idea." However, if the young person identifies with being upwardly mobile in the future, some are affecting a manner of speech that sounds sort of New England WASP, in my opinion. Perhaps, all part of the more fluid social mobility in the U.S.? Even ethnics might sound like news anchors with a non-regional, non-accent (news presenters).
Only in NYC and Philidelphia, I believe, natives to the cities pronounce "coffee'' as "coughee," and "water" as "warta." Elsewhere, water is "wahter," and coffee is "kaffee."
P.S.: I was too young to see the original films in the theater. The films were shown on tv for many years, they were so popular. The films during WWII reflected the supposed willingness of many to join the military, as the Bowery Boys were eager to enlist, in one film I remember.