CofE schools generally give some priority on admissions to families who attend church regularly. That is not the same as giving priority to Christians. Many families attend church purely to get a place at a church school. There is no requirement for continued attendance so many such families stop attending as soon as their child has a place.
And yes, there are church schools that have no church services and are staffed by people who are, on the whole, not practising Christians. They are by no means uncommon. As for encouraging Christianity or having overt acts of worship, to a degree that depends on your definition.
Remember that all schools are legally required to have a daily act of collective worship. Many schools ignore this but it remains a legal requirement. Even schools which ignore the requirement for a daily act of collective worship tend to have them at less frequently - weekly, for example. The contents of this act of worship vary. For non-faith schools the worship must be mainly or wholly of a Christian nature but faith schools can do whatever they want. Some non-faith schools will sing a hymn, for example, whilst some faith schools won't.
Similarly the syllabus includes RE for all children. The RE syllabus for schools in an area is drawn up by a local conference of teachers, churches, faith groups and the LA, and must reflect the fact that religious traditions in the UK are mainly Christian whilst also taking account of the teaching and practises of other major religions. Non-faith schools are required to follow this syllabus. Faith schools can draw up their own syllabus. Some faith schools use the same RE syllabus as local non-faith schools, some put in additional Christian content and a few choose to have less Christian content than the local syllabus.
As a general rule, church schools are not aggressively evangelical. They see their role as providing a good education, not turning children into Christians.