IF it's wood,it can be refinished. The real question is wherther you are up to the task. If you are willing to spend enough time and shed some sweat,you will likly get a presentable finish. You should be realistic about how well you need it to look because odds are it may look like a diy project. Not bad,just not equal to origional.
Ok,let's get down to the process. Is the top solid or veneered? Post pics of #1 face on of top #2 45deg close up shot where top meets table edge plus any unusual details. With that info,the good folks here at the web will ask more question and furnish more information than you thought possible.

Short answer, yes. When I was in the refinishing business, I did it all the time.

Stain matching color is an entirely different issue. As Jeff Jewitt, wood finishing author and supplier says, "When it comes to color matching there is simply no substitute for practice. And the practice will go more smoothly if you make some stain boards and understand some basic color theory to point you in the right direction."

The final color depends upon the natural color of the wood, whether it's veneer or solid, the stain or other colorants used and how you use them, the finish used, and the ambient light in the room.

And it's unlikely the current finish is varnish unless it was a piece finished or refinished by a non-professional. Lacquer is by far the most common commercial finish. Varnish is just too slow to dry, not adaptable to fast application methods like spraying and is not as repairable.