Yes, you should use the basket if you can. Problem is, a lot of times people get them off of ebay and the baskets have been lost so there isn't much choice. I would fabricate something out of coat hangers or something if I didn't have a basket. This will make a difference if you are actually using the thing to clean stuff.
Think of it this way; the ultrasonic generator is sort of like an electric palm sander, it just runs at a much faster/higher cyclic rate. You know what happens if you put too much downward pressure on the sander, right? It stops it from moving or slows it down. You will notice that the basket hangs from the top so the weight is not on the tank, it's not sitting on pegs or anything on the bottom of the tank. That is for the very reason I described before. That weight could overload the generator, make it run hotter and the extra load slows it down to a less efficient speed. Now mind you, if it were a little bitty gold necklace or something, it would make little difference. But 60 and 120mg glass bottles... that's quite a bit of weight for the dainty little generators in these things that aren't designed for it.
And don't get me wrong, I'm not saying it won't work if you do it, I was just getting the warming out there to people that this could shorten the lifespan of the unit.