No. me- is the marker for what is variously called the Immediate Past or the Perfect "tense" in Swahili. It expresses an event in the recent past whose effects are ongoing in the present. This corresponds most closely to the English Present Perfect, formed using 'have' and the past participle, i.e. "has bought".
With inchoative verbs that express a change of state, the English translation may sometimes use the Simple Present. Thus nimelewa (from the verb kulewa "to become drunk") could be translated as "I have become drunk" (Present Perfect) or "I am drunk" (Simple Present).