Technically yes, but in practice it's not that simple. The term labor aristocracy exists for a reason. A minority segment of the working class can be bribed to sufficiently align their material interests with those of capital. On a personal level you can really observe a shift in the mentality of someone who reaches a certain level of wealth, even if they are still technically workers, when their lived experience diverges so much form that of the average working class person, when their material interest becomes tied to maintaining that level of wealth, when the people they surround themselves with are also within the same elevated social strata. They begin to develop a real petty bourgeois mentality that aligns with their non-working class social and material conditions, regardless of how they earn their income.
I know the relation-to-means-of-production purists don't want to hear this but this is a real psychological and social phenomenon that we do ourselves a disservice to discount. It's because this is not always understood that some Marxists get confused as to why so much of the western working class is as reactionary as it is, but you cannot get the full picture just by looking at class in the strictest orthodox Marxist definition alone.