There's a part directly related to the koinonikon. According to the Georgian ms the verses which were recited before the communion (cf. modern koinonika) are as follows:
O taste and see that the Lord is good. Allelouia.
I will bless the Lord at all times.
O magnify the Lord with me.
Come unto Him, and be enlightened. Allelouia.
Glory to the Father. Allelouia.
Both now. Allelouia.
Let us receive the Body and Blood of Christ,
let us taste the fountain of immortality. Allelouia.
I will bless the Lord at all times.
O magnify the Lord with me.
Come unto Him, and be enlightened. Allelouia.
Glory to the Father. Allelouia.
Both now. Allelouia.
Let us receive the Body and Blood of Christ,
let us taste the fountain of immortality. Allelouia.
Then there are other things following, but they aren't indespensable for our purposes.
The verses above are possibly abbreviated and maybe also the Allelouia is left out after some verses for brevity as it is usual in old mss, but it's obvious that the hymn which is strikingly similar to the koinonikon of Pascha has Allelouia. This I guess resolves the issue.