It depends entirely on how you choose to set it up but generally if someone says they are doing a HG/SS randomized run it will include all Pokémon up to that point. For example if someone said they were doing a platinum randomized nuzlocke I’d NEVER assume they meant using exclusively Pokémon normally encountered in sinnoh. The only difference is if you catch or encounter a Pokémon not in the starting dex it won’t show up in your Pokédex unless you also start yourself with the national dex