Does early intervention have any effect on the development of logical thinking and reasoning skills of deaf and hard of hearing?

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Yes, early intervention has great effect on the development of logical thinking and reasoning skills in children with hearing impairment.
From birth to 3 years of age is the critical period. Early intervention has great effect on speech and language development of the child. Early intervention helps the clinician to take the advantage of neuromaturation, the period at which learning speech and language has great importance in child's life.
Hearing is critical for the development of speech, language, communication skills, and learning. The earlier that hearing loss occurs in a child's life, the more serious is the effect on the child's development. Similarly, the earlier the hearing loss is identified and intervention begun, the more likely it is that the delays in speech and language development will be diminished. Recent research indicates that children identified with hearing loss who begin services before 6 months old develop language (spoken or signed) on a par with their hearing peers.