would they even be allowed to

I don't know what this means. Allowed by who? A sovereign country can do anything it wants and is practically capable of doing. Nobody can forbid them from doing anything. All that others can do is impose consequences. The question to ask is what would the consequences be of Russia taking such an action?

The "judicial system" is also irrelevant here as well because how are you going to enforce their ruling? The ICC charged Putin and it meant absolutely nothing. They charged Netanyahu and it meant absolutely nothing. International law only has power over countries that cannot defend themselves.

Another example is the DPRK. They were not "allowed" to have a nuclear program. And this wasn't just a farcical colonial institution under the control of the West like the ICC saying it, it was the UN, the only institution that formally has the legitimacy to pass and enforce international laws. But the DPRK did it anyway. They accepted the consequences and that was that. Short of an actual invasion what could anyone do to stop them?

It's not a question of legality or what you are "allowed" to do, but simply of what you can do and get away with and what others can and are willing to do to you in return.

In this case you have to consider potential military retaliation, nuclear escalation, diplomatic consequences with global south countries, etc. Some countries would react more strongly than others. Some would acknowledge Russia's legitimate cause to retaliate, others wouldn't. Some would just protest but do nothing. Just how some countries choose to recognize the legitimacy of the ICC verdicts and some don't, and even of those that do many do so in word only.

It's the same with NATO's "Article 5" by the way. A lot of people are under the impression that somehow these sorts of treaties just kick in automatically once conditions are met and every country has to obey them. But that's not how it works. Countries have to make a political decision whether to acknowledge that conditions have been met, whether to abide by the treaty or not, and if so how. There's a lot of bluster now but when it really comes down to it how many will chicken out?

International law, international treaties...sovereign countries are not really bound by any of that stuff. Sovereign countries are free to break or selectively obey any law or treaty they wish, depending on their overriding interests and political imperatives. They just have to calculate how others are likely to respond and whether that is acceptable to them. The only thing countries are really bound by is the limitations of their own power, their political, military and economic might to convince or coerce others.

At the moment Russia seems to have decided that hitting the West directly would cause more trouble than it's worth, because they are winning anyway so why rock the boat? But they can always change their minds.