Most probably did, although there is always some uncertainty. This is what a new study demonstrates almost beyond doubt.
Tatiana M. Karafet et al., Improved phylogenetic resolution and rapid diversification of Y-chromosome haplogroup K-M526 in Southeast Asia, EJHG 2014. Pay per view → LINK [doi:10.1038/ejhg.2014.106]
It also demonstrates that "Australasian" haplogroups M and S, as well as several other K sublineages from that area belong to the same subhaplogroup, "brother" of P and "cousin" of NO.
The sample, focused in SE Asia and Oceania, is quite massive (4413 K-M526 samples) so there is very limited chance that further studies will produce major changes in this understanding. However there are some geographic blanks like Myanmar which can produce surprises when they are finally properly studied. Mitochondrial DNA from the Bamar (ethnic Burmese) showed in a recent study to have very high top-level diversity, suggesting that their ancestors played some key role in the formation of the peoples of Asia and beyond.
But while we await for those future studies or even the political chance to perform them, let us see what this excellent paper can tell us.
First of all the new data allows for a re-drawing of the K haplogroup tree, including renaming proposals:
For easier understanding, I annotated in red the new version of the tree with the populations carrying each of the sublineages in SE Asia and Australasia (but excluding island Oceania because of its recent colonization date and simplicity). I also annotated in green the proposed timeline of formation of various nodes downstream of K, per this study:
The presence of so many basal haplogroups and paragroups (signaled with an asterisk) in Island SE Asia makes compulsory to accept that K2 (formerly known as K(xLT) or MNOPS and right now listed in ISOGG as just K) but also its descendants K2b, K2b1 and K2b2 (P) must have originated in what is now the Malay Archipelago but was once a large emerged peninsula known as Sundaland.
This is my reconstruction of the likely centroids of K2 sublineages (named) and the K2* paragroup (stars):
The map originally included several work layers in order to analyze the geographical scatter of the downstream haplogroups within K2b but, for visibility reasons, I chose to to make them invisible.
Instead I made the following map of approximate plausible routes for the various sublineages of K2:
I must say that K-247, labeled as K2e here but reported as close relative of NO in a previous study, which named it "X", and which is found only in India (reported in two men) may add some extra complexity to the K2a (NO) arrow. It is for example possible that K2a'e and P migrated northwards jointly, splitting ways somewhere in Indochina (K2e migrating to India with P1 and maybe some already formed Q remaining in Indochina as well). This matter however requires more investigation and so far other possibilities such as later independent minor flows between South and SE Asia are equally likely.
Although not detailed enough to capture the nuances of the rare basal sublineages found in the various populations of Island SE Asia, this map may be of help for some in order to illustrate the importance of patrilineal haplogroup K-M526 globally:
Overall this study underlies and vindicates my repeated claim of SE Asia playing also an important role in the formation of the Asian+ branch of Humankind, together with South Asia. Something I have repeatedly suggested is that mtDNA macro-haplogroup N appears to have coalesced in SE Asia, while its most prolific "daughter" R instead seems original from South Asia, but that both have left a legacy East and West of the Brahmaputra regional divide.
I am not sure on how exactly couple mtDNA N/R with the spread of Y-DNA K2 but it seems almost certain that they are related to a great extent.
I also suspect that the Toba supervolcano catastrophe may well have caused enough damage to allow for a sudden expansion of one or several human populations after it. I would think that the Toba catastrophe marks the beginning of the expansion of Y-DNA K2 and mtDNA N, although it is quite possible that some other lineages like C were also involved in secondary roles in this secondary, yet so influential, expansion in Asia and Oceania.
Another possible element which may have aided this expansion could be dog domestication, which, although so far cannot be documented before 33,000 years ago in Altai, is suspected to have happened first in SE Asia.