Mathias, in answer to your question, no, this is not possible.
The bearing in question is a separable roller bearing, and the only practicable way to extract the outer race is to remove the core plug on the rear face of the gearbox housing (see photo below) and tap the old race out. The new outer race is installed from the inside - the race has a shoulder that buts up against the inside of the gearbox housing wall and holds the upper shaft in position longitudinally. It's at this point that you deal with the upper gearbox seal located on the output shaft (output shaft already removed in the photo below). It may be possible to extract the old race from the inside, but if the aim is to fix not just the failed bearings but the two seals as well, then separating the gearbox from the rear axle is only way forward.
I recommend replacing the lower gearbox seal (located in the PTO housing) when you have the gearbox free from the engine and rear axle. You can then flip the gearbox upside down, meaning that you are not fighting gravity when disassembling and reassembling. The PTO housing is no lightweight, and on reassembly it has to be eased rearwards as it is engaged into the opening on the underside of the gearbox housing. This is not easy if you are trying to do it whilst lying under the tractor.
Another reason for stripping the gearbox as shown below is that you can give the housing a thorough clean ready for the new oil that you will wish to refill the gearbox with.
Long story short - the gearbox needs to be separated from both engine and rear axle.
Good luck!
Best, Adrian.
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