What a fun question. I have a simple answer...NO. Gees louise. For drainage that ALL plants need (except for aquatics) you HAVE TO HAVE A DRAINAGE HOLE. Terrariums work only if there are enough roots to suck up water, water is rarely added and very sparingly. The terrarium is covered to inhibit evaporation and increase humidity. The plants that survive a terrarium are either transitional aquatics or cactus.
Plants (except for the specialized aquatics) need air in the soil. The water displaces the air. If there are enough roots the plants can suck up and transpire the excess water to encourage air pockets in the soil.
I've gone through this perched water table thing made by us humans thinking that gravel, sand, pebbles, rocks provide drainage. It is the furthest thing from the truth. Soil with small pore spaces on top of rocks, gravel, sand, styrofoam peanuts with large pore spaces, the small pores of the soil have to become saturated before water even begins to move into the large pore spaces. And THEN where does the water go? Stagnant, breeding pond of scum that most plant roots hate and rot. Saturated soil has no AIR.
Herbs, NO WAY. Sure you might get a bit at the beginning but it will be short short term. Drainage, air are critical for most plant health to include herbs. Got to have drainage and that means a hole at the bottom of the soil. No rocks, gravel, chunky monkey anything beneath the soil. Soil and then hole at the bottom. Raise the bottom of the pot off the surface with tiles, never allow plants to sit in water (we do that in intense heat and that is ok out of doors)...I hope this helps. Growing plants in terrariums is one thing, growing herbs in half a terrarium is completely another. DRAINAGE is critical. A dang hole is critical. There are ways to drill holes in glass. But why use bottles?
Finally. I found an article JUST ON THIS SUBJECT. Actually two; gravel beneath potting soil
This one is about how pots without gravel at the bottom deal with potential for perched water table, excellent article on pore spaces, air spaces, gravitational potential which is opposite matric potential perched water tables in pots