In part. When a new company moves in, it directly creates employment, and employees purchase stuff and pay taxes. So yes, the taxes that the employees will pay partially pays for any subsidies. Then the money that the employees spend creates more jobs, which in turn results in more tax revenue, which also can go towards the subsidies. An the money that those employees spend creates even more jobs and more tax revenue, so on and so forth. It's really not that hard to understand.
That said, I don't think that the government should ever subsidise any private business. It's essentially unfair to the businesses that don't get subsidised, and all of the new jobs creates wage inflation which may be good for the workers, but its not so good for businesses. So for every businesses that moves in due to the subsidy, another business may get choked out of the market. Many years ago my county and state gave away huge subisidies to BMW, a month after BMW annouced that moving to my county was a done deal, a half dozen other large employers who were considering my county annouced that they were removing my county from their short list - due to their fear that the labor market would be to tight after BMW hires 3,000 workers for their new plant.
It's odd, you would think that subsidising private companies would be a liberal idea, but it's not. Without exception, everytime the issue comes up in my state, it is always republicans pushing for it. Just recently our republican governor, Nicki Hailey, pushed our state government to make Amazon.com sales tax exempt in order to lure them in. I contacted my local state representative (a republican) and asked her why they would do such a thing, she said that the supported it because it would bring in jobs and tax revenue. She went on to explain that we are better off with lower taxes. I asked her if she supported the fair tax, she said "yes" and went on to explain it's virtues. So I then asked her why, if sales tax is preferable to other types of taxes, would you support eliminating the sales tax requirement inorder to collect more from other types of taxes, and if it was good for one company needed to be sales tax exempt, then why wouldn't we want all companies in our state tax exempt. She asked me if I was recording her, I told her that I wasn't, she then said "Good day" and hung up.