The generalization states that: The occurrence of syllabic liquids in a language almost always implies that of syllabic nasals. Is this true for English? let me know your thoughts. examples would be greatly appreciated.
The question is not well formed.
"The occurrence of syllabic liquids in a language almost always implies that of syllabic nasals" is what is called a "linguistic universal" (a misnomer), specifically a "statistical universal": it is making a statement about languages as a whole, and saying that we should expect to find relatively few languages that have syllabic liquids but not syllabic nasals.
Therefore, to determine whether this kind of statement is true, you need to look at a statistically representative sample of all languages: you can't say that it is true or false in reference to the single language of English.
The situation in English would be one data point that could be used along with others to either support or refute the universal.
What we find is that English has both syllabic liquids and syllabic nasals, so it is not a counterexample to the stated universal.