Yes. You can look at the thickness of the wires and count the number wires and look at the colours, feel the weight and look at the type of construction, but you cannot determine anything accurate. If you know where the transformer came from and have a similar one in a project and have a lot of comparisons, you can say two transformers are similar or equal or identical.
But in 50 years I have never "messed around." You don't know if the transformer has been thrown out because of leakage, spikes, a shorted turn or hum and buzz.
This type of list has never been prepared because it has never been needed. Transformers rarely fail and when they do, the product gets thrown out too.
Out of 35,000 TV repairs maybe 1 or two transformers were replaced and these were from voltage doubling TV sets where the transformers ran very hot.
And only one stereo amplifier transformer.
If you want to test a "power transformer" Connect 2 x 30watt transformers back-to-back to produce a 30w isolating transformer and connect the primary of the transformer under test. If the transformer draws current, it has a shorted turn or is not designed for say 240v. You can read the output voltage and fit a globe up to about 20watts to determine the current.