Andre, the air will come out overtime, but if the oil is severely aerated you can damage the pump running it like that.
It is best to change the oil if it is really aerated, a friend's logsplitter would work great when cold, but would start to get sponge after he ran it for a few hours. After a couple of years of use he was complaining that the splitter ram was stalling quite often. I plumbed in a tee and got pressure readings a full rpm and in high and low gpm. According to Barnes the pump was worn out.
After buying a new pump and installing a filter on the return line. I decided to change the suction strainer also since the hydraulic tank had been drained,The strainer was clean and while investigating how the tank was built I discover that the return line was not under the operating level of the tank. The oil being returned to the tank was being aerated. I ground the welds off the top of the tank and added a drop tube to the tank and his problem went away.
There was a grayish coating on the bottom of the tank that had to be from the wear to the pump.