Fruit tree cross pollination

This is probably a very silly question, but If I plant both a greengage tree and a plum tree in my garden that are in the same pollination group and therefore will cross pollinate, will I still get pure greengages on one tree and pure plums on the other tree? Thanks

My experience is as a consumer not a grower. I buy fruit from what's left of the small orchards in this area. The plums and gages are always true to type in spite of growing several different varieties. 

If the cross pollinated fruit came to maturity  their offspring would be different. 

I'm sure someone will put me right if this isn't the way it works.

Greengages are just a type of plum for a start.

the effects of crosspollination are only apparent when the seed is sown and grown on. Think about it. the fruit a plant produces is determined by the genetics of the plant. So a rose always produces a Rose hip of a particular type, as does a variety of Apple, Plum ,gooseberry, blackbberry and so on.

Many thanks all of you.