Hello Adrian
I don't know if it's allowed by the manufacturer. But I do it anyway. I think that's also quite normal. It would be daft to do everything twice. A cleaning agent is also supplied. I use a typical parquet care product diluted with water.

Hello Adrian

As long as the care product does not foam and is not sticky, there is nothing to stop you using the machine. On the other hand, you should pay attention to whether your parquet is oiled/natural or sealed/varnished. If it is oiled or untreated, I would not use such a machine. Although it is apparently not a microfibre roller (no go for parquet), the combination of material, many revolutions and wetness is likely to damage the parquet. I wouldn't take the risk. Oiled and untreated parquet may only be picked up "damp" at most - then apply the care product with a cotton / parquet mop for a more even finish. The Dreame tends to be too damp, especially if it is operated slowly or left standing for a short time. Test: if a drop of water is absorbed very slowly and/or leaves a dark stain, keep your fingers away from the solution.
If the parquet is sealed / varnished, it is not critical - and in this case no expensive wood preservative is necessary. Hope this helps. Greetings, André