Can a non-Catholic faithful go to confession to a Catholic Priest?

As confession is often looked suspiciously at by many non-Catholics, there still exist a good number of non-Catholics who would like to go to confession.
These non-Catholics are not actively engaged in some protestants program and still do not intend (in the near future) to become Catholic.
Aside from the many graces received during confession, non-Catholics may also be interested in the psychological benefits of telling someone else their sins and the relief they might get when hearing the words of absolution.
So, is it permissible for a non-Catholic to get in the line of the confessional and kneel before a priest ready to receive the sacrament of reconciliation?
In this case, the Code of Canon Law is fairly straight-forward about the sacraments of the Catholic Church. As the Church recognizes the baptism of most Christian denominations, the valid performance of the sacrament of confession is recognized only within the confines of the Catholic Church (with the primary exception being the Orthodox Church).
On almost all occasions, to licitly receive confession, one must be a professed member of the Catholic Church.
So according to the Code of Canon Law (Can. 844 #1), Catholic ministers administer the sacraments legally to only Catholic members of the Christian faithful, who likewise receive them legally from Catholic ministers only.
Though, there are some cases where an Orthodox Christian can receive the sacrament of confession as well, since this branch of Christianity has valid sacraments.
Yet, the Code of Canon Law gives a list of a few exceptions for baptized non-Catholics.
So, in accordance with the Code of Canon Law (Can. 844 #4) it says that, If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians that does not have full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
Fundamentally, a Catholic priest can offer absolution to non-Catholic Christians in certain rare cases, such as the danger of death.
However, non-Catholic Christians are certainly encouraged to seek out a Catholic priest for spiritual counseling, and can do so in the context of a scheduled meeting at the parish office.
Though, in most cases they should not approach a priest during a regularly scheduled time of confession in the church building. These times are reserved only for members of the Catholic Church and do not allow the proper time for catechesis or extended personal advice.
Moreover, Confession is a beautiful sacrament, one that can free a person from sin and set them on a new path.
So to embrace this gift fully, one should be properly catechized and be fully initiated in the Catholic Church.