Hi,
No.
The iMessages server do what is Called a "push" of the iMessages towards all devices that are "registered" with the iMessages server.
It will do this for a few days only (I have personal experience of picking up iMessages on a Sunday evening on my Mac having has a conversation on my iPhone on the Previous Friday (about 48 hours) It may be a long enough period to handle a whole week end but I have no experience to prove that.)
An iPhone that is Airplane Mode or Off completely for a period will "de-register" from the iMessages server as will a Mac.
On an iOS device you can quickly enter the Settings and see when the iPhone Number becomes Verified again.
This is a little more difficult to see on the Mac as a support app called IMAgent does a partial Sign In to "Listen" for new messages before you launch the app.
9:17 pm Saturday; March 29, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad