but will they buy bitcoins with that money?
Why not? Reports have been made after the very first release of stimulus before that some people in the US are actually buying Bitcoin. Though, only a small percentage of that total amount could be added to the Bitcoin market, but at least it has made a noticeable impact.
Top researchers are eyeing some stimulus could be put to either stocks or Bitcoin.
They definitely will, not everyone of course, but some definitely will. Think about it this way, consider how many people are in crypto in USA, and consider 10% of those people putting all their money in, even that creates a huge increase in bitcoin price.
However one thing is a big problem that not many people consider, the reality is that we are in a situation where it doesn't go to every single citizen all at the same time, it just goes in parts by parts and that means that we will not see a huge increase all at once, and that is why I think the price will not be affected that easily, sure it could be something that can make some money, but it doesn't mean that it will make that kind of money right away, the price will change upwards a bit, but it will be gradual increase and not all at once, the more people get their checks the higher price will become.