No, don't put any oil base stain under the acrylic paint. The paint will start peeling in just a few months. Stain is a completely different type of product and can't be used as a substitute for priming.
Use oil base wood primer, thinned slightly for better penetration. This will seal the wood and stop excessive tannin bleed. Allow the primer to dry, min. 24 hours. If any areas are showing some bleed through use Zinsser Cover Stain to seal these areas.
This will give you a good foundation for the paint and a paint job that will last.
An alternative is to use a solid color oil base stain, like Cabot's O.V.T. Solid. In this case, do the needed prep and apply 1-2 coats of the stain. Personally, priming and painting will give better longer lasting results.