Yes. ‘air’ will always be entrained in steam, to some extent,
Air is roughly 79% Nitrogen and 21% Oxygen, with a little CO2 and some other elements or compounds that we don’t need to consider here (i’ll refer to all of the above as ‘gases’).
N2, O2 and CO2 are all soluble in water. Therefore, if you introduce Raw Water (untreated Towns Water) into a boiler, it will contain ‘air’ which are these gases, dissolved in the water.
Now the real bogey-men here are Oxygen (O2) and Carbon Dioxide (CO2) which will accelerate corrosion of the boiler when they come out of solution. For this reason, industrial scale boiler use several methods to reduce these deleterious gases before they enter the boiler and cause harm. Typical methods would be deaerators to drive off the gases, or chemical ‘scavengers’.
The amount of oxygen in the steam is dependent on the steam pressure. At my work, we were making 850 psig steam and needed very high quality water to reduce corrosion in the steam system. The deaerator uses trays to would reduce the oxygen content to below 5 ppb. Oxygen scavengers would remove the remaining oxygen. The steam produced would have no oxygen.
This is for a high pressure industrial boiler. A lower pressure boiler would not have as much water treatment and would make steam with more oxygen. Boiler water in an industrial power boiler should not contain more than 20 parts per billion Oxygen.