Is the word "gandharva (gandhabba)" related to the conception of an embryo?
No. The word Gandharva is not related to the conception of an embryo.
Gandharvas are a type of celestial beings. They are recognised as celestial musicians in the court of Indra along with the celestial nymphs.
A Gandharva named Viśvāvasu has been mentioned several times in the Rig Veda and also in the Shatapatha Brahmana. He is the king of Gandharvas. His special duty is to guard Soma. For example:
The middle stick he lays down first (on the west side of the fire), with the text 'May the Gandharva Viśvāvasu lay thee around. (Shatapatha Brahmana 4.2)
उदीर्ष्वातः पतिवती हयेषा विश्वावसुं नमसागीर्भिरीळे |
अन्यामिछ पित्र्षदं वयक्तां स ते भागोजनुषा तस्य विद्धि || Rig Veda 10.85.21
udīrṣvātaḥ pativatī hayeṣā viśvāvasuṃ namasāgīrbhirīḻe |
anyāmicha pitrṣadaṃ vayaktāṃ sa te bhāgojanuṣā tasya viddhi ||
Bound for the world of life immortal, Sūrya: make for thy lord a happy bridal journey. Rise up from hence: this maiden hath a husband. I laud Viśvāvasu with hymns and homage.
Gandharvas are many times mentioned in epics like Ramayana and Mahabharata also. But they are not told that they are related to embryos.
Hence, they are not related to the conception of Embryos.
By observing the text you have quoted, the word Gandhabba could be synonomous to Kandarpa. Kandarpa is another name of Kāma, the god of Love. He is the reason for the birth of an off-spring.
Quoting from Srimad Bhagavad Gita:
āyudhānām ahaṃ vajraṃ dhenūnām asmi kāmadhuk |
prajanaścāsmi kandarpaḥ sarpāṇām asmi vāsukiḥ || BG 10.28 ||
Among weapons, I am the Vajra (thunderbolt). Among cows, I am Kamadhuk; among progenitors, I am Kandarpa (the god of love). Of dragons, I am Vasuki .
And Kāndarpa is a person related to Kandarpa. A child is born when a father, mother and their love is combined. So, the word Kandarpa can be related to conception of embryo.
Above paragraph is just a guess. I might be wrong though.