Depends on the surgery and the results. My doctor has rung me with some before now for things like when a test came back suggestive of glandular fever.
I'd ring in any event to check. My surgery have someone who gives results out once the doctor has seen then and you have to select a specific option on the phone line which is only open certain times.
If something shows up though I imagine they will want to speak to you about what happens next. No blood test can conclusively diagnose arthritis - even if a rhumatoid factor is done and shows up then it isn't necessarily conclusive as it can show up in a number of conditions. Other tests can show up inflammation (eg ESR/CRP) but not where, why etc...
Let us know how you get on, there are quite a few of us arthritis suffers on here.