Tomato, Tomahto?

Around three and a half years ago I moved to San Antonio Texas, and currently live in a county called Bexar. A quick piece of history for those concerned; San Antonio was once called San Antonio de Bexar. When I first moved to San Antonio I found, to my surprise that Bexar is pronounced 'Bear', like the animal. This got me thinking: 'Bexar' and 'Mexico' are both spelled with an 'X', but 'Mexico' in the Spanish vernacular is pronounced with the 'X' silent substituting it for an 'H' sound; therefore in 'Bexar' the 'X' is also silent and pronounced with the 'H' sound. Now in the American English vernacular the 'X' in 'Mexico' is not silent. So, should the 'X' in 'Bexar' be pronounced in the American English vernacular?