If you thin the ink then you will reduce the glossy effect. I have found that, for FW inks, 1:5 dilution reduces the shine and much more eliminates it.
As I mostly use inks to wash into low areas I often use much higher dilutions to produce a more subtle shading. Even 1:30 has enough effect to make a difference without taking the top tone down.
What I have found is that heavy ink washes can lift when varnish is applied and colour the varnish coat. Rarely enough to matter except over light colours but it happens.
Tony of TTT