In my experience, no.
That's why they make the tinted version of the danish oil - so you have
options in terms of what hue you wish to achieve. I just finished a cherry
high chair to which I applied 5 coats of natural Watco danish oil. To the
high chair tray I applied 3 coats of satin wipe on poly and the color
changed imperceptably (at least IMO). This was a good thing, for me, as I
loved the color I achieved with the natural oil.
I have used dark walnut and cherry watco before, and I know they have a lot
of other shades. You might want to get a few of those and try them out to
see if you can get what you're looking for.