Jumping in as one of my kids was diagnosed with dyslexia this year. Because he's in French immersion we had A LOT of questions about the intersection of second language learning and dyslexia.
The psychologist who did the testing was very clear that a lot of the strategies that work in one language will work in the other (obviously not those related to orthography, but other techniques and skills!). He strongly discouraged us from moving out kid to a unilingual stream. Essentially, French will follow once his English improves.
Basically, if you can adapt in one language, you'll maybe not be "fine" but will often be able to adapt in another, just with more effort than others and the same type of accommodations.