Does a child have a choice when it comes to being indoctronised?
There is of course, always a choice, but most younger children are under the perpetual (and powerful) influence of their parents, making it incredibly easy to force a child into the choice the parent wants. Even if the child chooses to resist whatever religion is being taught to them, however, their parents can still force it upon them. The child does have choices (most of which he/she cannot comprehend), but very few can prevent a parent, with a strong intent to indoctrinate the child.
Can a child know they are being indoctronised?
I don't want to generalize about children as a whole, but, at young ages, I'm sure they won't even know what indoctrination is, nevermind know it is happening to them. Their knowledge is limited to what their parents deem appropriate to show them so scrutiny on the part of a child (scrutinization and questioning are what separate education and indoctrination) is a virtual impossibility.
Can a child avoid being indoctronised?
It again depends on the child itself, and, more importantly, how old they are when the indoctrination is begun, but in most cases, I would say no. Parents have tons of influence on a child, and it would take an incredibly strong-willed and self-assured one to resist the influence of both their parents, and the religion's community as a whole.