if the surface of the probe consists of pure metal (not corroded, no coating), then the microwave radiation will be virtually completely reflected by the probe, and thus will not increase its temperature. Therefore, the probe will be at the same temperature as the fluid, provided that the thermal energy drawn off by the connecting cable is negligible (the cable should have a small cross-section). I assume that the thermometer itself is placed outside the oven. So, in short, it should work.
However at the outset, you might want to make some comparing measurements; for example, heat the fluid until the thermometer shows 50°C, switch off the oven and open it, put a small, fluid based thermometer into the fluid and compare both thermometers. Or better still, if you can manage to put a color changing thermo indicator into your fluid, you could observe the color changing during the heating up of the fluid, and compare it with the thermometer reading.
I agree regarding the high frequency current but sparking occurs only if the current path is interrupted or partly of high resistance, or, as in Marian Costea's video, if the shape of the metal forms resonant structures in close proximity or with sharp edges (the fork tines). The former can be the case if you put gold plated china into a microwave oven, for example. But in normal operation, no sparking occurs despite the fact that the oven chamber is made from metal.
As you wrote, connecting the probe to earth is not necessary but does no harm.
If necessary, one could suppress microwave current on the cable outside the oven by ferrite clamps.
I need to measure the viscosity of my fluid under irradiation simultaneously. but I can not find a service center for this experiment. So do you know where to do this? or any idea to do this in the microwave?
One could purchase a stock viscosity meter, shield it appropriately in a perforated cage, immerse that assembly in the fluid of choice, and irradiate it with microwaves.
I have some experience of the vibrating reed type of sensor - not cheap, but fairly compact.
https://allesco.com/products/rheonics/
You could also calibrate a hand-built sensor against fluids with the same density but known viscosities. Something as simple as a slotted rotating vane. Drive a motor coupled to a slotted vane at constant speed and note the power needed, as a function of viscosity. Apply that rotating vane to the unknown fluid, in the microwave oven, and deduce the viscosity.