No, because:
>The real question is whether people who already are employed would stop working had they received "free" money.
So: will unemployed people stop looking for a job if they receive free money?
That's not quite the question. The question is, will unemployed people look less for a job if they're guaranteed free money even once they get a job, compared to the status quo where they are guaranteed free money (for awhile) that stops once they get a job.
There's also a follow-up question, that is something like "Will people on permanent disability start getting jobs if you stop punishing them by permanently taking away disability payments if they get a job?"
That destroys your argument.
Feeling like you can loudly assert things not in evidence is a sign of some pretty tall ideological blinders.
But a hypothesis is just that: a hypothesis, not a fact. There's plenty of existing research on how changing unemployment benefits change work incentives (answer: not too much), but it's also true that longer time horizons might change that answer. That's why experimental tests are needed.
edit: the whole system is more complicated than this, of course, but the point here is that this safety net is permanent – you can not lose it even if you are unemployed for a long time (recently, a tiny reduction of welfare payment was introduced for those who do not meet certain criteria for activity; however, you are in any case entitled to certain level of income, and government-paid rent, etc., in any case.)
Also “will people be more likely to start their own enterprises if they have basic income?”
I know a few people who live in some of the most expensive areas of the country and are permanently unemployed, they live fine (although not a lifestyle that I'd want) and spend their time pursuing creative endeavors. They do have to do things like grow their own vegetables and brew their own beer to save money. You get different benefits depending on age, disabilities, if you have children (and if they're yours or if they have disabilities), partners, etc. For the general unemployment benefit you have to be going to job seeker support and looking for work, but some people are just not employable (for instance if they have drug convictions).
It's worth noting that this social welfare system was put in place under a conservative government, when we had a more liberal government we had state support for artists as well with no restrictions.
It's hard to give exact numbers as a monthly income because unemployment benefits are broken up into cash and vouchers and credits. For instance in NZ if you're unemployed or poor the government will pay your rent, give you cash, subsidise a lot of your expenses, give you vouchers to use at the supermarket, etc. The state and city councils also own housing for the poor and unemployed.
In addition the system is administered by private industry who are rewarded based on number of interviews, not placements.
I would hold up Australia’s unemployment welfare system as a prime example of what to not do.