No.  It's been asked for, but there's been no word about adding it.

You can modify ElementalDefs.xml to do it....

        <!-- Unit grouping type upgrades -->
        <EnableUpgradeGroup>1</EnableUpgradeGroup>
        <UpgradeGoldCostPerTroop>10.0</UpgradeGoldCostPerTroop>
   

You can even use it to up the group size of some quest units.  It will give you an "upgrade" option just like weapons and armor though.  The exploit could be building strong units at size 3 and getting a relatively cheap, fast upgrade.

I don't understand why level should decrease for upgrading unit size as opposed to upgrading equipment. Both of them make your unit more effective.

That's not a balance argument. 

Also, damaged units replenish with presumably new troops when they heal. 

Well, then there's really no issue -- if you modify your ElementalDefs as above, then you can upgrade and it doesn't affect level.