It can, yes, although this does depend on the type of speech problem your child has so do ask your child’s speech & language therapist for their opinion. Phonology problems are more likely to and often do go along with difficulty reading and spelling. As described in the previous question, Phonology is a bit like a computer program that tells your brain how to break down words and how to add sounds together to make words. If there is a ‘bug’ in that computer program, you are likely to have problems first with speech, then with reading and writing.
Early treatment by a speech & language therapist can help reduce the impact of a speech problem on literacy learning.