Nope, not connected to the Murray's except that George Murray was, supposedly, from Dumfriesshire, Scotland; so there may be a very distant kinship.
A quick look of George's family, which may or may not be useful, follows.
GEORGE MURRAY b. Scotland ca. 1806, m. Richibucto, Kent Co., NB 27JUN1838 FRANCES (FANNY) MARSH (b. England ca. 1817).
In Weldford Parish, in 1881, the households of James Murray (36) and of 'Willim' (37) and Amanda (34) Murray were listed next to each other. With James were Mary (27) and David (23) and a widow, 'Fanie' Murray (64), presumably their mother. I do not find a comparable person in the 1871 census, nor, in 1881, do I find William Robert Peck; although he is in Kent Co., in 1882.
There was, in Weldford Parish in 1861 a Frances Murray b. England ca. 1816. There was also a George b. Scotland ca. 1806, presumably her husband. When George Murray married Frances Marsh both were of Weldford Parish. This suggests the Murray's and Beck's may have been connected as Janet Beck m. Richibucto 3AUG1835 George Marsh. William Beck m. 28AUG1849 Eliza Marsh; both of Weldford Parish.
A Mrs. Mary Murray (b. ca. 1818, d. 5JUN1857 age 39 years) of Weldford Parish m. Richibucto 3NOV1840 Alexander Morton. Possibly the Alexander Morton (b. 1822) who m. 1st Mary Burton.
1. JOHN MURRAY.
2. WILLIAM MURRAY b. ca. 1845, m. AMANDA _____ (b. ca. 1847).
3. JAMES MURRAY b. Molus River, Kent Co., NB 17JAN1844 (ca. 1845), d. Kouchibouguac, Carleton Parish, Kent Co., NB 15FEB1947 age 83 years.
4. MARGARET MURRAY.
7. MARY MURRAY b. ca. 1851-4, m. at her father's home, Molus River, Kent Co., NB 2AUG1882 WILLIAM ROBERT BECK (b. ca. 1854), s/o Robert and Elizabeth (McDougall) Beck..
Next door to William's family, in Weldford Parish, Kent Co., NB in 1871, was that of William (26) and Amanda (24) Murray. On the other side was the family of James (26) Murray. This suggests a fair-sized family in Weldford Parish. James' family appears to consist of his siblings, Mary (20), Eliza (18), Ann (16) and David (14). When married, Mary was the 4th daughter of George Murray. Presumably William, James and James' siblings were also children of George Murray. James and family were 'Scotch'. There was also a widow, Catherine Murray (b. Ireland ca. 1801) living with Robert (31) Kinsilla and his brothers. There were other Murray's in the parish in 1871 as well, so some care needs to be taken in assuming relationships.
71. NINA BECK b. Harcourt Parish, Kent Co., NB 10FEB1887.
72. FANNY ELIZABETH BECK b. Kent Co., NB 12APR1889.
73. ELEANOR BECK b. Mortimre ('Mortimer'), Kent Co., NB 21MAR1891.
74. ANNIE MAY BECK b. Harcourt Parish, Kent Co., NB 10APR1893.
8. ELIZA MURRAY b. ca. 1853.
9. ANN MURRAY b. ca. 1855, m. ALBERT EDWARD POWELL.
J. DAVID MURRAY b. ca. 1857-8, d. Kouchibouguac, Carleton Parish, Kent Co., NB 26AUG1889 age 32 years.