You can certainly make it, but it won’t taste like mead. It’s more of an earthy, slightly sour wine. There’s a place that made some for a sale a few years ago, but I’m not sure if it’s still made.
If you want to give it a try, you’ll need to add some yeast nutrient to get healthy fermentation. I recommend using a hydrometer so you have some control over the residual sweetness and alcohol content. For example, if you want something around 8% alcohol, dilute the syrup to 15 Brix. If you want it to finish sweet, use a yeast that dies out below the maximum potential alcohol.
For your first batch, just start with syrup, yeast, and nutrient. Once fermentation is complete, you can take small samples and experiment with additives like lemon juice, fruits, or spices. You can play around with adding stuff during fermentation in later batches, once you figure out what tastes good.
As CarnalK said, there’s a huge variety of stuff that not made from those sugars, isn’t distilled, and is delicious. Besides the obvious beer, there’s also plum and pear wine, which is quite popular. Blackberry, blueberry, and strawberry wines aren’t as common but can be very good. On the other hand, cane and beet sugar are almost always used for distilled alcohol.