Is it true that the letter "g" is silent in the English language if it comes before another consonant and "es" is often silent as well?

I think you have to be extremely careful in trying to create a general rule from that sort of situation.  The main cause for that odd pronunciation for the spelling is due to changes in language over time, often due to a separate language group having to do with the origin of the term.  There is no global rule that applies to particular circumstances.

The peculiarities of the history of Britain (multiple waves of different linguistic-ethnic groups over fairly short periods) is more important a cause of this oddity than a generic rule that is employed by the English language.

No.

counter-examples: grow, glow, eagle, egret, agree

When a word begins with "gn..." then the "g" is silent.

examples: gneiss, gnu, gnarly

With the combination "[vowel]gh" the g is normally (not always) silent.

example: night, weigh, lightning

I can't think of any instance in which "es" is silent.

First of all, pronuniciation of British English and American English is quite different. For example, the word "lieutenant" is pronounced "loo-tenant" in the US, and "lef-tenant" in the UK. If there is a town called "Gneglestogn", it would probably be pronounced "negleston" in the US, although place name pronunciation is determined by the local population. "Houston" is "hewston" in Texas, but "House-ton" in Atlanta where it's the name of a street. But yes, there are words where the g is silent before a consonant, as in the animal name "gnu" which is pronounced "new". "Es" would not be silent in any US pronunciations that I know of.

Worchestershire, which many people don't know HOW to pronounce, is properly pronounced "wooshtersheer" with a soft "r" in British English.