Nope
Kurgan Hypothesis is based upon R1b and R1a
Anatolian hypothsesis is based upon G Hp no matter how low the frequencies are today
J2a and j2b is still an opponent or an ally of G,
First of all there were neither R1a nor R1b haplos when Kurgan hypothesis was postulated. Secondly current Kurgan hypothesis presumes that IE invaders were predominantly R1a since for a while no R1b was found in kurgans.
Anyway I think that both Anatolian and Kurgan hypothesis can be right. Now when we have ancient autosomal data from Iberia and Sweden we can easily reconstruct the so-call IE invasion in Europe.
Now we can reasonably assume that North-European component (Dodecad K12) belonged to hunters-gathers with y-dna N1 and Mediterranean component (Dodecad K12) belonged to hunters-gathers with y-dna I and distribution of these components in Europe approximately mirrored current distribution: Western Europe heavy with Mediterranean component and Eastern Europe heavy with North-European component.
On the basis of the above made presumptions we can make the following conclusions:
a) R1a guys before entering Central Europe should be heavy with Caucasus component (Dodecad K12), which they most likely picked up in Anatolia when moving from Near East to Balkans.
b) R1b guys before entering Western Europe were heavy with Gedrosian component (Dodecad K12).
In this case we can make up a scenario of IE invasion:
1) R1a guys enter in Balkans from Anatolia heavy with Caucasus component (probably ~ 8000 BP) and settle in Balkans for a while.
2) Groups of R1a guys start expansion from Balkans in Central and Eastern Europe pushing away and genociding hunters-gathers with y-dna N1 and I taking their women for breeding (one male on several females) thus deluding their Caucasus component with North- European and Mediterranean components (probably ~ 6000 BP).
I guess R1a-z283 guys moved to Central Europe while R1a-z93 guys moved to East(Pontic steppes).
Scenario of R1b guys migration:
R1b guys moved from somewhere in Near East. They were heavy with Gedrosian component. I guess they divided on three groups: the first group moved to Africa (V88), the second moved through Anatolia (L23) but was stopped by R1a guys on Balkans so they could not enter Western Europe and were dissipated and assimilated by different people on Balkans, Greece, Anatolia and Caucasus, the third group used sea route from Near East to South France. Since the third group did not move through Anatolia it did not pick up Caucasus component. That explains why Basques do not have Caucasus component but only Mediterranean, North- European and Gedrosian components. From South France R1b guys started expansion in the West Europe pushing away and genociding hunters-gathers with y-dna I taking their women for breeding (one male on several females). Later some groups of R1b guys (Bell Beakers) were assimilated in Central Europe by IE R1a guys (CW) and so R1a guys passed Caucasus component to R1b. Then these groups of R1a/R1b gangs invaded Western Europe populated mostly by R1b guys spreading Caucasus component and IE language. It looks like Basques were not involved in this process since they did not gain Caucasus component. No Caucasus component no IE language.