MBP with no serial number

Question

I recently had my logic board replaced on my 2 yrs old MBP.  I also had the bottom case replaced due to a dent (unrelated)  and ever decreasing gap on the superdrive slot.  The top case was also replaced due to a trackpad issue and defective sticky key.
On it's return from the local Apple Store, the memory showed defective and the apple store told it needing replacing but given it was a 3rd party upgrade (4Gb) it was not covered. I checked the memory and seated the 2 modules (both unseated) and all was well. I also noticed that all the lables in the battery bay were missing. Not too concerned but thought something may have been there - Bar code, MAC Address etc
Last night I was checking a few things and noticed that my serial number is now showing as  "System Serial#"  There's no number now. Should i be concerned that I have a MBP with no serial number? 
All repairs were carried out at an Apple store in the UK, so genuine repairs, though you'd never guess it given the case fit and gaps

Answer 1

Iain MCClung wrote:
I take it then I will have no issues with . . . my time machine back ups?
You'll have a small one.  Time Machine doesn't use the serial number, but it does use a hardware identifier on, guess what, the logic board, to tell one Mac from another.  So on your first backup, you should get the prompt in #B5 of Time Machine - Troubleshooting.