I agree. This notion of question 2 providing a plausible cause that might lead to suspension v. question 1 where the test subject has to conceive of their own cause is a bias, but a different type of bias, not a conjunction fallacy. There could be (and possibly have been) ways to construct the test to control for this. For example, there are 3 test groups where 1 and 2 are the same and for the third, the two events are asked independently: What are the probabilities of each event:

A. That USSR invades Poland, or B. That US suspends relations

I believe this is not a conjunction fallacy, but for a different reason. In the first case, the test subject is required to conceive of a reason that might lead to a complete suspension of relations. There are many different choices, invasion, provocation, oil embargo of Europe, etc. Each of these seems remote, that the test subject might not even contemplate them. In the second case, the test is given a more specific, therefore more conceivable sequence of events.

A good third scenario, to control for this, would have been to ask another group of subjects the probabilities independently:
A. That USSR invades Poland B. That US suspends relations

This provide the same trigger of a plausible provocation, but doesn't directly link them. Variances between the estimates of B in this case v. 1 in the original test would indicate confidence interval between variances between 1 and 2.

You describe the millionaire daydream as a sink. That could be reframed as an opportunity cost. The same as any short-term v. long-term gratification, the time spent daydreaming may create an opportunity cost wherein the preoccupied brain isn't investing in some other opportunity that could lead to higher returns in the future, such as your technical school example. This simply restates that the costs of the lottery ticket are the lost marginal utility of the dollar which could have been spent on, or invested in something else, plus the opportunity cost of the lost time spent daydreaming that could have been spent on something else. The benefits are the marginal utility derived from the time spend daydreaming.

In that regard, it still seems that the purchase may be good for some, if they can afford the dollar, they enjoy the daydreaming, and the determine that the opportunity cost is low. It all seems to hinge on the individuals utility functions for the dollar, the daydream, that the expected future value of the rewards associated with the alternative time lost to daydreaming.