Yes there is a few, according to data collected by Humanist from Family Tree DNA and 23andMe, 2.7% of Assyrian men carry Q1b.
N=113 09/09/13
25.7% R1b
18.6% J1
15.9% T
13.3% J2
8.0% E1b1b1
8.0% G
4.4% R2a
2.7% Q1b
1.8% R1a
0.9% F
0.9% L
Printable View
Genetically, they are certainly not Levantine. Their Eurogenes SPA point was not far from that of the Assyrian point, which was near Babylon.
Also, regarding your comment about the title of "rabbi." My grandfather was also a "rabbi," or "learned one / leader." In Syriac/Sureth, as in Akkadian, no particular religious significance was (is) attached to the title of "rabbi," or "rabi."
A few Akkadian examples:
http://i1178.photobucket.com/albums/...passuru__1.jpg
http://i1178.photobucket.com/albums/...abi_bari_1.jpg
http://i1178.photobucket.com/albums/...uhatimmi__.jpg
http://i1178.photobucket.com/albums/..._akkadian_.jpg
They are Babylonians who did not get Persianized or Arabized:)
https://scontent-b-ord.xx.fbcdn.net/...73305434_n.jpg
https://scontent-b-ord.xx.fbcdn.net/...02047966_n.jpg
https://scontent-a-ord.xx.fbcdn.net/...57924412_n.jpg
https://scontent-b-ord.xx.fbcdn.net/...64747034_n.jpg
https://scontent-b-ord.xx.fbcdn.net/...15965594_n.jpg
https://scontent-a-ord.xx.fbcdn.net/...60139905_n.jpg
https://scontent-a-ord.xx.fbcdn.net/...78696386_n.jpg
https://scontent-b-ord.xx.fbcdn.net/...12974998_n.jpg
https://scontent-a-ord.xx.fbcdn.net/...07954364_n.jpg
https://fbcdn-sphotos-e-a.akamaihd.n...49032888_n.jpg
https://scontent-a-ord.xx.fbcdn.net/...69813113_n.jpg