Not with Audacity. Audacity does not support artwork in metadata.
You could use the free metadata editor “MP3Tag” (Mp3tag - the universal Tag Editor (ID3v2, MP4, OGG, FLAC, ...)) to add the artwork after exporting from Audacity.
This feature request was logged some time ago (Metadata: Embedded album art and lyrics metadata discarded · Issue #1505 · audacity/audacity · GitHub), though it is closed for now with the comment:
“Improving metadata handling is not planned for the moment, closing for now. There may be a bigger metadata release eventually, follow #1464 for that.”