No, the multicolored trim with blue was present in the mid and late 1960's.
I was able to check my yearbooks and media guides from the 1950's and 1960's. The uniform pictured in the auction has a narrow red, white, and blue trim around the neck, arm openings, and down the side. The uniforms worn during Chet's era at Bradley do not appear to be exact matches. Also, Chet was a big man, and it would have been difficult for him to fit into a Size 44 uniform top anyway.
The side stripes in the early 1960's appear to be thinner than the one pictured. After Chet left Bradley in 1962, Levern Tart wore #31 for the 1962-63 and the 1963-64 season. Then the trim stripes got a little wider. A player named Ted Osman wore #31 for 1 season, (1964-65- the only season he played for BU). Then Joe Allen wore #31 from 1965-1968. Joe was also a very big man, and it seems this jersey (size 44) might be a little small for Joe, too. The #31 on the front of the jersey appears significantly larger on the auction jersey than on any of the BU jerseys worn in the 1960's. I seriously doubt this jersey was worn by Chet Walker.
There was no #31 on the 1968-69 team, and then Rich Schultz wore #31 in 1969-70, 1970-71, and 1971-72.
After Rich Schultz in 1971-72, nobody has worn #31 on a Bradley varsity team since!
The Bradley all-time numerical roster reports that Derrick Parks wore #31 in 1984-85, but that appears to be an error, as the media guide shows he wore #41. Also, this Bradley site says Ben Coupet wore #31 in 1994-1996, but that is apparently also an error, as according to media guides and my memory, Coupet was #00 for both years he played at Bradley.-
https://www.nmnathletics.com//pdf8/...SID=608647&SPID=1498&DB_LANG=C&DB_OEM_ID=3400 (page 7)
I do not think this jersey matches any of the ones from the 60's, and thus is not likely Chet Walker's jersey.