English orchid was borrowed from the scientific name Orchideae, which is from Latin orchis "any of various kinds of orchid" - early botanists misinterpreted the Latin stem as ending in -d-. The Latin word was borrowed from Greek ὄρχις "testicle", from Proto-Indo-European *h₁erǵh- "to mount" (AHD).
Also according to the AHD, *h₁erǵh- in the suffixed o-grade form *h₁orǵh-eyo- became Greek ὀρχέομαι "to dance", and ὀρχήστρα "in the theatre the space on which the chorus danced" - which was the earliest meaning of orchestra in English.
Pokorny has two roots: *orĝhi-, *r̥ĝhi- "testicle" and *ergh- "to shake, tremble" - the latter is the source of orchestra. Connecting both roots with the meaning "to mount", as the AHD does, seems a stretch to me.
The OED says the etymology of ὀρχέομαι is uncertain, and says its derivation from Pokorny's "to shake, tremble" is "unsatisfactory".