As Laurel points out, the process of forming new words by appending prefixes and suffixes is called morphological derivation. Not an arbitrary process, it follows certain idiomatic conventions, either phonetic or semantic, that assure that a new coinage looks, tastes, and feels like English. When it doesn’t, you can term it “illegal,” “nonidiomatic,” or, if it suits you, just plain wrong.
The first criterion is whether an affix is still productive, i. e., it is still used to form new words. Pro- and anti-, for instance, are highly productive; be- as in bedraggled or bedazzled is not. I suppose ante ‘before, prior to’ might be glued onto some Latin root to come up with a new word, but chances are good no one is going to say they need to make a phonecall *antebreakfast.
You can at least assure your friend that em- is still productive in modern English. When commercial aviation became a thing in the 1920s, for instance, industry-specific terms were coined for getting on and off: thus enplane/emplane and deplane were born.
The emplane/enplane variation brings up a phonetic rule for your friend’s favorite prefix: em- is really en- assimilated to a root beginning with a labial consonant, b, p, and sometimes m. That means it can never be attached to a root beginning with a vowel or any other consonant. This eliminates such attempts as *emgolden. The rule would generate engolden:
About the same time the royal palanquin stood at the palace portal, engoldened, jewelled, and surmounted with a panache of green plumes. — Lew Wallace, The Fair God, 2018 (orig.1873), 51.
Staying with colors, empurpled already exists:
vnwares it [a knife] strooke into her snowie chest,
that litle drops empurpled her faire brest: Edmund Spenser, The Faerie Queen, 1590. EEOB
Today, one also encounters the word in a metaphorical sense:
Firbank's spoofing is altogether too silly, too empurpled, too doting to sustain the mood of correction essential to satire. — Robert F. Kiernan, Frivolity Unbound: Six Masters of the Camp Novel, 1990.
Purple prose is flowery, extravagant writing, which means if you use a word such as empurple, you’re more than halfway there — as in this early 20th century poem about the San Gabriel Mountains of California:
Where range upon range the Sierra lies dreaming a-swim
In the stillness of April, the warm golden splendor of light,
Enrosed and emblued and snow-summitted height after height,
Bathed in silence and color… Sunset Magazine 16/4 (Feb. 1906)
As far as I can tell, neither enrose nor emblue has an entry in any dictionary: they are nonce words created just for this poem. But because they follow the conventions of coining such words, any reader would understand them. Whether this is a literary success is up to the reader to decide.
You may have noticed these en- color words occur in quite formal registers — poetry of varied quality or a well crafted sentence in a novel — and all breathe the air of earlier centuries. Excellent writers might get away with resurrecting them or coining new ones; merely good writers might be better advised to avoid them.