Yes, you are correct. All TAD's with logo's have a serial number. TAD Kohara started using serial numbers in 1978. He started to use his logo in 1983.
TAD cues use weights built into the front and rear section of the handle. Removing weight from the rear of the cue at the butt cap would definitely be the wrong way.
Word of advice, most of TAD's cues from that time period were 20oz - 21oz. That was about the standard weight range he built them. There are cues with different weights by customer request, but those requests were rare. If the cue is indeed 19.5oz which is more synonymous with the standard weights of modern day cues, it would be safe to make the assumption that the seller isn't the original owner, had the cue refinished, and the weight changed. Just something to consider.