Hyperwarp
Captain
...
SAC isn't even using Salut engines so why do you think they'll use Saturn engines? The engine preference of SAC goes like this: Liming engines > Salut engines > Saturn engines. The second option hasn't even been taken so Saturn isn't even in consideration right now.
SAC has no dealings with MMPP Salut from what I know. Salut deals are exclusively for CAC (J-10 and J-20). Those Salut engines are customized for CAC.
In contrast J-11/J-11A made by SAC uses AL-31F from NPO Saturn. So the question is whether Russia is now willing to sell AL-41F1S to SAC?
So when it comes to Russian engines it it something like,
Salut -> CAC
Saturn -> SAC
Soloviev -> XAC