The actual answer is a bit complicated and depends on a lot of things.
In general, the answer is no, with exceptions, but the number of exceptions can be large, due to bilateral or multilateral agreements.
In Europe, one of the most popular treaties is the CEPT recommendation T/R 61-01. Read the actual file for details, but in general, if you're within the CEPT area, you'll need to add the prefix for each country, but your own call-sign would remain the same and you'd just need the CEPT license, if you have the class 1 license in Austria. Don't forget that some countries still want Morse code exam for their license.
Also, prefixes can get a bit complicated if you're using a device which limits the number of characters in the callsign for APRS.
Things get a bit more complicated once you leave the CEPT area, that is to say, when you leave Russia. In general, you'd need to check if each country (you didn't list them, so...) has some sort of bilateral agreement with Austria and see how it would go to get an amateur license in that country. In case of some countries, you might get a short-time license with prefix plus your own callsign, like DL/XX1YYY in case of Germany, while in others you might need to get a real local callsign. This can also get a bit complicated, if the foreign administration wants to go into details of your examination, has requirements on how long you need to be in the country and so on. For example, in some countries, if you're Norwegian, and have an Austrian callsign, your Austrian license won't get recognized, but a Norwegian license would have been. Don't forget about the recognition paperwork and the potential fees that could be quite high. Some countries might also charge frequency usage fees as well.
In the opposite case, situation is a bit worse: You'd need to get your Cambodian license recognized in your European country and then hope that they will issue you a CEPT license, so you can use the CEPT license in Europe.
Also, don't forget that APRS only works if you have good APRS coverage, so don't forget to take that into account!