Yes, there is definitely theological meaning to the seamless woven garment (John 19:23). The mention of the garment tells us the Jesus was acting as High Priest. The High Priest wore such a garment at Passover. In fact, without the garment, the priest was not fit to serve (Ezekiel 44:19). The garment is not the ONLY thing that makes the priest fit to serve, but it is a MUST. The Levitical priests all wore this garment; it is mentioned specifically in the narrative telling of king Saul's order to Doeg to murder 85 priests (1 Samuel 22:18). Mentioned elsewhere I am sure.
So Jesus is BOTH the Lamb AND the High Priest who offers the Lamb (himself). Jesus was crucified "at the sixth hour" (John 19:14). That was the very hour in which the High Priest began the slaughter of the Passover lambs in the Temple.
Interesting also that at Calvary, while on the cross, Jesus is still presiding over the Passover meal that began MANY hours earlier. FOUR cups of wine were taken at the Passover meal, but only THREE cups are consumed before Jesus abruptly gets up and leads the apostles to the garden. The "cup after supper" (Luke 22:20) was the third of four cups consumed at the Passover meal. The four cups were to recall the four "I will" promises of deliverance made by God to Moses in Exodus 6:6-7 ("bring you out," "rescue you," "redeem you," and "take you as my people" (NKJV)). The third cup is often called the "cup of blessing" or the "cup of redemption."
The FOURTH cup is consumed after the Great Hallel (the singing of Psalms 114-118). Mark 14:26 and Matthew 26:30 tell us that they sang a hymn before going "out to the Mount of Olives" (NKJV). Having controlled EXACTLY when the wine is served to him on the cross (John 19:28-29) Jesus drinks the fourth cup and then says, "It is finished," meaning the Passover meal is finished. Not a priestly function (or is it? not sure?) but another illustration of how deliberate and in-control Jesus was in performing his various roles even on the day of his death. In praise and thanks!