I think your a bit confused on your terminology (it could be me, but I am confused a bit about what your saying),
You can have a MAXIMUM of 1 extended partition on any harddrive.
You can have a maximum 4 primary partitions. These are "real" partitions, as dictated by the limitations of the ancient 286 bios.
Generally you make 3 partitions primary, and then make a 4th primary partition be the "extended" partition.
From that extended partition you divide it up into logical (pretend, sortof) partitions. That way you can get past the limitations of the x86 bios.
Now you can have as many logical partitions as you wish. There is a limit somewere, but I think it's fairly high.
However you CAN'T have 2 extended partitions. Only one.
So if you have a setup like this:
120gig harddrive:
4 partitions:
1=20gigs
2=20gigs
3=20gigs
4=40gigs,
And you make partition 4 the extended partition so then you have
5(logical)=20gigs
6(logical)=20gigs
So you have a total disk space aviable of 100gig divided up into 5 accessable "drives". Which are not drives, but Windows calls them drives incorrectly for some perverse reason.
Drives = physical devices
partitions = what harddrives are divided up into.
That means you now have 20gigs that you can't ever use for anything. You used up your primary drives, and did not alocate it to your extended partition. If you did then you would still have that 20gigs aviable to partition into more logical drives.
So no, you can not alocate that extra space to a extended partition since you can never have more then one extended partition. I think that you can probably alocate it to a primary partition (since you have 2 extra that you seem not be using), but it'll mess up the drive numbering sceme. Linux can deal with that, but it's confusing and I don't know if windows can deal with it.
Either way, you can try.
However if I am confused and you do indeed have that space alocated to the extended partition, and haven't just gotten around to making it into a logical partition, then yes, you can install linux into a logical partition.