Could the logic analyzer with less than 136 channels be used for the 4x clocking mode?

Could the logic analyzer with less than 136 channels be used for the 4x clocking mode?

Yes.  However, part of the channels on the probe head would be disable for transferring the signals and used for the storage only.  If you have the TLA7 NA 4/AA4/AB4/AC4/BB4/BC4 modules, you could use the 4X demux probe P6964 which has 4 probe head connectors that you could use all 136 channels for all 34 channels on the target footprint for the 4X mode.