Does your dominant language proficiency determine the degree of possible proficiency in L2?

This question is based on fundamentally flawed assumptions about what 'language proficiency' is. The key things to remember are:

1. Language proficiency is not a binary state. You can't say that you either have it or not. Everyone is proficient in some ways and not in others.
2. There is no maximum language proficiency. The label 'fully proficient' has no basis because language is not finite.
3. Language proficiency cannot be measured along a single progressive state. You always have to define what you are able to accomplish in a language with what level of accuracy and fluency. (The ACTFL levels are a very good guide to what this might look like.)
4. Language competence may not be manifested in all contexts equally. So a speaker will find it easier to draw upon their underlying competence with vocabulary, morphology and syntax in certain situations than others. For instance, speaking at a conference vs. renting a car.
5. Not all aspects of language may exhibit the same level of 'proficiency'. Most often it is the pronunciation that is seen as deficient but morphology, idioms, etc. will also be subject to localized issues.

The above holds for L1 and L2.

Being aware of this, you can formulate an answer to your question:

1. There are many situations, in which an L1 speakers may find it easier to communicate about certain areas in L2. They will have the right vocabulary but also know the right ways of formulating their thoughts.
2. There are cases of variable regression so a speaker will loose some of their L1 and L2 will become their main language. This is often seen in emigres.
3. It is possible even for people with severely impaired L1 to acquire L2 in many contexts. E.g. differential educational opportunities. In cases of underlying language impairment, the person may exhibit the same deficiencies in L1 and L2.
4. People often have prejudicial views of their own language proficiency which they equate with 'knowing the grammar'. Therefore, they may be assuming that because they know more about the 'grammar' of one language, they know the language better. Similarly, native speakers often label educated non-native speakers as speaking 'better English' than them because they use certain constructions and choose more formal vocabulary.