I did a bit of testing with 2 wire antennas this weekend. Here is a summary of the results, which I also posted to the IC-7600 e-mail reflector:

The antennas:
1 – A “long” 80m Dipole, ladder line, 4:1 balun, then a long coax run
to the rig
2 – A fan dipole with 80/40/20 meter elements (these are close-spaced
elements, with 80m and 40m using opposing legs of a single piece of
300-ohm twinlead), 1:1 balun, then a long coax run to the rig

This was a brief test. I tried only 10/15/20/40/80 meters, and tested
only a few frequencies on each band, including something close to the
bottom and top of each band.

The IC-7600 internal tuner was able to tune both antennas over most of
the 10/15/20/40/80 meter bands with the following exceptions:
1 – Could not match the 80m Long Dipole at the high end of 80m or
anywhere on 40 meters
2 – Could not match the Fan Dipole anywhere on 20 meters

The External LDG-100 PROII was able to match all the test frequencies.
The IC-7600 tuner is very good, and tuned most of the frequencies,
including some that appeared to be worse than 3:1 SWR (the stated
spec) on my antenna analyzer.

Please note – I am NOT knocking the internal tuner, and with a little
antenna work (pruning antennas and feedlines – not fun) I could
probably get matches everywhere I need to operate. So, while the
internal tuner is very good, the LDG (which has a nice ICOM interface)
covers a wider range. The LDG was sometimes very slow (10s of
seconds), but once a match is found it is stored and recalled quickly
next time you need it.