...will Recovery HD be functional (and backed-up) by so doing?
Recovery HD isn't a
part of OS X, rather it's a completely
separate animal and will NOT, therefore, be backed up by Time Machine, nor will TM's running or not running during its installation have any effect on it...SHOULDN'T under expected circumstances, anyhow.
You can see in this Terminal excerpt that Recovery HD is a volume unto itself.
Artie's-MacBook-Pro-2:~ artie$ diskutil list
/dev/disk0 (internal, physical):
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *500.3 GB disk0
1: EFI EFI 209.7 MB disk0s1
2: Apple_HFS HD 99.5 GB disk0s2
3: Apple_Boot Recovery HD 650.0 MB disk0s3
4: Apple_HFS HD2 299.9 GB disk0s4
5: Apple_HFS HDx 50.0 GB disk0s5
6: Apple_HFS HDz 49.6 GB disk0s6
Artie's-MacBook-Pro-2:~ artie$
I'm not aware of any means to back up a Recovery HD other than with Carbon Copy Cloner.
Any other pertinent TM input will have to come from elsewhere.