If you complete teacher training and a probationary year and gain QTS then you are trained for a particular age-group, but are qualified 'to teach'. Head Teachers have a lot of discretion these days as to who they employ, and indeed can employ non-qualified staff. At my school (secondary) we currently have 4 primary trained staff (mostly working with SEN), and I know in my boys' primary there is at least one teacher who started off in secondary. So it is possible!
Generally there are fewer jobs advertised in primary (though it depends on your area), so without primary training/experience you are less likely to succeed.
Similarly GTP/SCITT places in primary are in great demand. In practice (IME) they are usually taken by people with degrees who have chosen to work as TAs (or similar) for a number of years, and therefore have a lot of practical experience in the school.