I purchased the multimeter pictured below for a high voltage power supply I'm working on. It's rated for 100V DC and 10A, but I hope to measure several thousand volts. Is it possible to use a HV voltage probe like I would use with a regular multimeter on this component, or no?
No. Those cheap meters use a voltage divider adding up to around 280-290K and go directly into an 8-bit MCU (STM8 series).
Typical high voltage probes assume a reasonably accurate 10M\$\Omega\$ input impedance for the multimeter- something like 999M in series with 1.11M (internal divider values), so it would read grossly low on this kind of an input.
Only if the input impedances are the same to form a voltage divider.