Well, that’s a good question, a valid question, and the answer is, its probably not. It should be noted that The Way of the Pilgrim is popular devotional literature, but it never had the official standing of The Philokalia, and concerning it, Metropolitan Kallistos Ware remarked that the protagonist received the gift of unceasing prayer unusually quickly. It has also been recommended by many bishops to laity who wish to pursue hesychasm that they not attempt to do so without direction from a qualified elder, such as an accomplished monastic at a monastery like that of St. Tikhon, the main OCA monastery, or in California, their monastery of St. John Maximovitch or St. Barbara, Abbot Tryphon on Vashon Island, Holy Trinity in Jordanville, St. John the Baptist founded by Elder Sophronius in Essex in the UK, or the Athonite-style monasteries of Elder Ephraim across the US such as St. Anthony’s in Florence, AZ, or the monasteries on the Holy Mountain themselves.
Otherwise regarding the Prayer of Jesus, which can be said without persuing hesychasm, St. Ignatius Brianchaninov wrote a book about it, On The Prayer of Jesus, which should be regarded as an official and legitimate Orthodox document for laity published by the Russian Orthodox Church in the 19th century after the surge in popular interest in Hesychasm engendered by The Way of the Pilgrim.
I have this book, and would encourage any Orthodox laic who wants to practice the Jesus Prayer to obtain it with the blessing of their priest, for it was written specifically with the laity in mind. And also, obviously one should review their prayer rule with their priest, and also find out what their priest thinks about this issue, since between the different Orthodox traditions one might find slight differences of approach, and it makes sense as a general rule to use the one your priest knows.