The entire point of "separate but equal" was not to actually have equal systems, but to allow separation of white and black citizens to continue providing inferior services to blacks. This was not simply the case in 1950s America, obviously - it had been the norm since the beginning of the slave trade. "Equal" was essentially a constitutional workaround the Supreme Court found in Plessy v Ferguson - because of the Emancipation Proclamation which overruled the Dred Scott decision, African Americans had to be legally considered full citizens entitled, to the full range of benefits of that citizenship.

So, to answer your question as best I can - yes, it may have taken longer to overturn the separate but equal decision if the services had actually been equal. However, that was never the intention, and so the real target of the Civil Rights movement was not necessarily truly equal services that could remain separate, but actual equality - i.e., not separated (which inherently implies inequality).

Essentially, the inequality of services like schools was not a failure of the separate but equal system, but its intended result. It was a violation of the rights of black Americans both in concept and execution, and to fight for civil rights was therefore to fight for the overturning of that system.