Yes, it definitely does. The term onomatopoeia refers to the imitation of sounds in words. Therefore, when we say, 'The dogs bark,' we copy the sound they make by using the word 'bark.' However, when we wish to indicate that they made this sound in the past, we need to follow the conventions of grammar, to make the meaning clear. We therefore say, 'The dogs barked,' to indicate the tense. The fact that the sound is represented in the past, does not mean that the word has lost its onomatopoeic value.
Alternatively, one may say, 'The dogs did bark.' This convention, however, is outdated and regarded as poor English. It may also be ambiguous since the use of the auxiliary verb may be seen as being used in the indicative form, to assert that for example, they indeed barked instead of growling.
Interestingly, the word is, figuratively onomatopoeic, since it copies the sound a dog makes, but as a part of speech it is a verb, which indicates what action the dog performed. The one does not automatically cancel the other, since a word can have a dual function and may be understood both as a figure of speech as well as a part of speech. This duality is evident in many onomatopoeic words such as the following examples: the cat miaows, the horse neighed, the birds were chirping, the frog croaks, the crickets are chirping, etc