No it doesn't; not in terms of multi-decadal trends, at least, since there has been no strong multi-decadal CRF trend since the 1950s (and to the extent that there's been any trend, it has been one which would have a
cooling influence by the proposed cloud-formation mechanism).
Svensmark and Friis-Christensen almost explicitly state as much in their
2007 reply to Lockwood and Frohlich, not only by showing the lack of a strong CRF trend itself, but in the caption noting that the correlation becomes strongest
once the global warming trend is removed:
FIG. 2: The solar cycle and the negative correlation of global mean tropospheric temperatures with galactic cosmic rays are apparent in this ESA-ISAC analysis (ref. [2]). The upper panel shows observations of temperatures (blue) and cosmic rays (red). The lower panel shows the match achieved by removing El Nin ̃o, the North Atlantic Oscillation, volcanic aerosols, and also a linear trend (0.14±0.4 K/Decade).
Last I'd heard (which admittedly must be nigh on a couple of years ago now) the CERN experiments attempting to confirm the CRF -> cloud nuclei mechanism in the first place had still not achieved that result - the first of several stages in the process had been replicated, if memory serves.
[Edit: It seems Quaestio and Jack have some more recent information I'll have to look at sometime :lol: ] In time this apparent correlation might be upheld with a demonstrable causal mechanism. It may even end up being the case that galactic cosmic radiation variation has been a major climate driver in the geological past as Svensmark has proposed (though it should also be mentioned that even he acknowledges that CO2 tends to correlate about as well with geological temperatures as GCR does).
In the last half-century however, at most it might be responsible for year-to-year modulations of temperature with perhaps a slight multi-decadal cooling influence.