Of course. Even if a Latin Rite priest were available, there would be no problem with you receiving the sacraments from an Eastern Rite priest and having a Byzantine Rite funeral.
If you were in danger of death you could probably find an Orthodox priest to confess you. Finding a bishop that would allow an Orthodox funeral in an Orthodox cemetary would be a different issue entirely. Of course anything is no matter how unlikely is possible. It would depend a lot on where you were.
When my husband had a stroke and was in the ER facing death I asked for a Catholic priest to administer the Sacrament and the priest that came was Byzantine. A Catholic priest is a Catholic priest.
My husband recovered fully, thank God, due to timely and up to date medical care, and, of course the Anointing. Most people, physicians included, considered it somewhat of a miracle, but that is quite a story.
You most likely, however, would be buried from a Latin parish if you were not a member of an EC parish.
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