You may receive Communion in any Catholic Liturgy. You may also have your Confessions heard by any priest of any Catholic Rite.
Now if you mean practice Western spirituality in an Eastern Rite Liturgy, to a certain extent yes if you keep your devotions private. I still follow my First Friday Devotion because it is what mainly help me grow in my faith from when I was young. Just don’t expect the parish to have a Novena to the Sacred Heart or have an Adoration. I do still pray the Novena on my own.
Dear Constantine (the Great),
There are many UGCC parishes that have the Sacred Heart devotions and Eucharistic Adoration as you know.
I wouldn’t be surprised if someone from our Church came forward one day to assert that such devotions were first derived from the Christian East based on a revelation to a monk somewhere in the Thebaid during the first millennium . . .
Seriously though, the Sacred Heart has been, in a number of parishes, “re-constructed” in the icon of Christ the Lover of Mankind, either an icon of our Lord holding open a Gospel with His words of love or else the icon of Christ “Ho Eleimon” holding a Gospel with hearts on it and pointing to His Wounded Side (at least that is how it has been interpreted).
There are also Orthodox icons of the Mother of God “of the Seven Swords” and “Softener of Evil Hearts” where seven swords (of Sorrow, based on Simeon’s prophecy) are depicted on her icon and relate closely to the Western picture of the Immaculate Heart of Mary pierced with a sword.
In western Ukraine, there are Orthodox Churches with actual pictures of the Sacred Hearts, with Eucharistic Adoration and the Way of the Cross. I have in my possession a Ukrainian Orthodox booklet with the entire Way of the Cross in Ukrainian (but commemorating the Orthodox hierarchy) with a Foreward that urges “all Orthodox parishes to install the 14 Stations of the Way of the Cross!”
There are UGCC parishes and UGCCers (our brother Ciero is the one that comes to my mind most readily . . .

) who are more “Orthodox than the Orthodox” in a number of respects . . .
Alex