No, if they are homozygous for both blue and brown, they will lay green eggs and will breed 100% true to that.
There are many (at least 7, from what I recall reading) genes that influence the amount of brown pigment. Some interact and probably some are independent. Some increase and some decrease the amount of pigment deposited on the egg. It's all very confusing and could make producing a true breeding green egg layer non-trivial, but it's certainly possible to do. Isbars are an example of a breed that is true breeding for green eggs. They are not common, but I've seen them advertised on Craislist at least once in the Reading area, so definitely possible to obtain.
Thanks. It's good to know. I was so confused about how green egg layers can breed true, now I understand.