Welcome Doc_V to Sailnut.
I always use teak oil prior to using a finish like
varnish or Cetol. The oil makes the wood look great. Teak oil is also largely made up of Linseed oil which is one of the main components of most primitive varnishes. There should be no incompatibility between teak oil and
varnish.
I stopped using
varnish as it is too labor intensive and have switched to Cetol Natural Teak which holds up better. I find that even after oiling the teak and applying Cetol on top I have no problems with the finish coming up.
Of course, I like to let the teak oil seep in for about a week or two before I apply the more durable finish like Cetol. If I am in a hurry and can't wait I wipe the oiled teak down with Acetone on a rag and then start applying the finish coat. Wiping the wood down with Acetone prior to applying any finish is a good idea no matter how long the oil has had to seep in.
A caveat: teak oil will not make wood that has gone gray/silver with age look good unless it has been lightly sanded such that the wood is a more blond color. I have used a razor blade to take down the higher ridges followed by a light sanding with #220 grit sand paper and find that it is sufficient enough to allow the teak oil to soak in and create a nice ruddy (dark red) hue in the teak.
You might be amazed at how good your wood can look with a little prep work and some teak oil applied to it.