Not an issue.
A hydraulic reservoir should not be pressurised anyway except for atmospheric pressure.
Drain, and clean, is essential for weld quality anyway.
If you leave it full of fluid, yes it will exclude oxygen, but, what will the circa 900 deg C do to the hydraulic fluid, and the weld characteristics?
If you fill it with water, then that will also affect the weld quality and characteristics.
Having actually DONE this, IMHO your best option for safety, quality and reliability is to drain and clean, correctly, and then ensure that the weld zone is kept clear & clean during the procedure, then, for a machine reliability standpoint you must clean the reservoir appropriately after.
Remember you need to meet your ISO cleanliness standards for the hydraulic oil.
Can you ensure this if you leave the reservoir full I doubt it, if you fill with water I doubt it, if you pre clean, control & post clean, I would expect so.

You need to seal any incoming lines adequately.
You need to air the reservoir adequately, we did not purge, we simply aired the unit out.
The cleaning chemicals were solvent based and evaporative, the repair was to a porous/cracked weld, so we had to get the oil contamination, out of the weld.
The sort of things were "brake cleaner" type chemicals, and these were sprayed into the weld area after the majority of the hydraulic oil was cleared out.
The whole tank was in fact cleaned to a similar level.
Then it was aired with all 4 access hatches off for 24 hours, then welded, the weld was then mechanically cleaned with conventional hand tools, e.g. wire brushes, then it was solvent cleaned again with the residue being removed with suitable e.g. paper towels materials so that the cleaning materials did not leave a hydraulic system contaminant.
After the hot work had been done, the flammability issue had passed so the remaining hazard was from the cleaning chemicals.
e.g. solvent fumes.
This was easily managed and completed quite safely and worked.
However, we did have a fire marshall with extinguishers at the ready as a backup plan, and obviously the welder was in normal PPE./