Let us know what they say. I have sometimes wondered, after varnishing a painting, what if I want to change it? Would another coat of varnish afterwards keep it all together?
Unless you are certain that the varnish is acrylic, do not paint acrylic over it. Unless you use a special sealer over oil, acrylic will eventually flake off. I suggest you use a sealer. It’s called Zinsser Bulls Eye Clear Shellac Water-Based Sealer. It dries in less than an hour and can be painted over in a couple of hours. It’s available in a spray and as a brush on. I use cheap foam brushes when I cover yard sale discarded sofa paintings. They are usually cheap canvas but usually quality wood supports and reasonably good frames. Hope this helps.