No, it wouldn't be correct. It has to be "Does she know you?".
With words like "Does/Can/Will", the next verb has to be infinitive.
You can say "He jumps" but not "He can jumps" or "Can he jumps?" You say "He can jump".
In the same way, you can say "She knows" but not "Does she knows?". You use the infinitive "Know", "Does she know?"
We (Spanish native speakers) tend to make this mistake pretty often, it's because we are thought that for he/she/it should always add an s to the end of the verb but the way I easly learned it is looking at the Does part, you already added the third person corresponding s (if you will) so you're supposed to add such s only once in the sentence.
For example, if the does wasn't there you would then need to add the s to know: She knows you.
It is similar with past, we tend to say Did you liked it? when the first word in the sentence is already in past (the do itself) we don't need to change the verb to its past form anymore but we would need to if did wasn't there in the sentence.
The provided sentence is 'Она тебя знает'. The verb знает is the form it takes when we use either he, her, or it and therefor belongs to Она as present in this sentence. The last word in this sentence is тебя which is also used in the У тебя есть.. sentences that ask or state what the person 'you' has. So it can't be 'something that happened' because 'something that happened' is nowhere in this sentence.
We have 'she knows' and 'you'. If put in a question, then the only possible translation to this sentence would 'does she know you?' Does that clarify things for you?