I would say "no". Receive communion first, then eat the antidoron, then the bread blessed at the artoklasia.
+1
+2
In some old times there was much longer gap between the blessing of the bread during litiya and the Communion, so then it was not problem, but now it's obvious you should keep the Eucharistic fast. Nowadays maybe on Athos and some other Greek places (and Russian old believers) do not omit anything during All-night Vigil + Liturgy, so eating by them the blessed brad is truly to keep strength for the rest of the service and by eating it they don't break Eucharistic fast.