Not in the same as the RC way, no.
In Roman Catholicism, one belongs to a "Rite" inherited from one's Father or determined due to racial ancestry or conversion. If a Greek Catholic begins attending a Roman Catholic parish, that individual is still Greek Catholic and must observe the fasts and feasts and practices of the cannon law of the Greek Catholic Church. He might, for example, not begin fasting for up to several weeks after his co-parishoners begin to fast, and not celebrate Pascha until several weeks after they have celebrated Easter. In order to switch from being canonically Greek Catholic to Roman Catholic this individual would have to petition both bishops, undergo a period of transition (often a year or more, I understand), and then finally enter the Roman church. This isn't allowed, I have heard it, more than once or twice in a lifetime.
In Orthodoxy you follow the liturgical practices of the parish you attend. Thus my wife, Chrismated into Orthodoxy in the Western Rite, began practicing Eastern Orthodoxy when she moved to our area, attending a Greek church and so doing as they did. After she met me she began going to the Serbian parish that I attended, and practicing as we did. As an example of the change between the Greek and Serbian, she moved from the New Calendar to the Old. At no time did she require a letter to any bishop, an approval for attending and following a different calendar, etc. She just said goodbye to Father Stephen of St. Michael's, hello to Father Jim of St. George's, and then hello to Father George of St. Peter's. I've had many friends do such switches.
I don't know what you mean by "status"? It's an approved Rite within the Antiochian and Russian churches, and anybody received by their churches is considered Orthodox by any priest I've ever met with. It's very small, has some people who don't care for it, seems to be growing, as far as I can tell, is undergoing a change in the Russian church to bring it more into line with canonical regulations on such things as ordinations at one Liturgy, and is widely approved of by every Orthodox my age I've ever discussed it with.
