Maybe someone else can say yes for sure, but I can at least say that quite likely yes. If there is a counterexample, it would be an extremely remarkable number.
You were wise to include goldbach-conjecture. If the Goldbach conjecture is true, every even number greater than 2 can be expressed as the sum of two odd primes in at least one way.
What's more, every even number greater than 6 can be expressed as the sum of two distinct primes in at least one way. According to the OEIS, these are the only even nonnegative numbers that can't be expressed as a sum of two distinct primes in two or more ways: $$0, 2, 4, 6, 8, 10, 12, 14, 38.$$
Also allowing nontrivial prime powers (hereafter just "prime powers") helps out a little if we require the summands to be distinct: $$6 = 2^2 + 2$$ $$10 = 2^3 + 2$$ $$12 = 3^2 + 3 = 2^3 + 2^2$$ $$14 = 3^2 + 5$$ $$38 = 3^3 + 11$$
Among the small numbers, primes are more frequent than prime powers, but we can still observe that as the numbers get larger, more options become available.
So while 14 and 38 have fewer options than 12, 140 and 380 both have more than 12, though maybe not as many as 120.
This effect with primes is the Goldbach "comet." It's not strictly increasing, but the running average is. Throwing prime powers in the mix surely fortifies the comet.