No. However, some Poskim[1] allow doing so. Some Poskim[2] rule one may rely on this opinion in a case of need. According to all one may not walk outside of the room before washing.[3]
[1] Shvus Yaakov 3:8 in name of Rashba rules the custom is not to be careful against walking four Amos being people consider the entire house as four Amos. [Shaareiy Teshuvah 1:2] Thus according to this opinion one may walk around the room before washing; See regaridng a single room being considered four Amos: Shach 344:11 in name of Mordechai end of Moed Katan; Beir Hagoleh in name of Mordechai; Beir Heiytiv 344:8; Elya Raba 1:4; M”B 45:2 in name of Ateres Zekeinim; This opinion is omitted from Admur ibid
[2] Shaareiy Teshuvah 1:2; M”B 1:2
[3] As only the room is considered like four Amos according to the lenient opinion and not the entire house. [Peri Megadim 4 A.A. 1; Ashel Avraham 4; Beis Baruch 2:2; See however Daas Torah 1]