Since this is a lab type boiler intended for students to do thermodynamic experiements, any air trapped in the boiler will effect the results of their experiments. The presence of air will not cause the boiler to over pressure and explode. Air is compressible and less likely to over pressure the boiler than one completely full of water. The boiler is protected by a safety relief valve so the likely hood of an explosion is extremely small,
The air will expand wth the heat creating pressure. You boilers water outlet is most likely near the bottom, thus not allowing the trapped air to escape. This could lead either to a rupture or complete failure of the boiler
Oil Field's answer is good, but I would like to add that as air contains oxygen, it can lead to corrosion of the boiler. For this reason commercial boilers have equipment to deoxygenate feedwater. Also some inject hydrazine. For a small boiler just venting steam will carry out the air. You use the CSTR equation to calculate how much to purge to get a certain O2 level.
