I see that the Cantonese connection has been brought up already

I wouldn't go as far as to say that "all the country names that uses 加 to transliterate a hard G or K sound is due to Cantonese influence."
Let's look at "Canada" as an example.
加拿大 in Cantonese is ga na dai [ka na tai] (汉语方音字汇). This transliteration, if from HK Cantonese, would be abnormal. But, it isn't from Cantonese; it's a Huayu original.
Wiskey 威士忌, on the other hand, did come into Huayu from Cantonese. HK Cantonese = [uɐi si kei] .
Here's a list of HK Cantonese loan words. Not all of them are in Huayu. After looking through them, you should know why 加拿大 didn't come from Cantonese. The segments in the brackets are IPA. p = b in pinyin; p' = p and so on for k, k', t, t'.
巴士 [pa si] bus
啤啤 [pi pi] baby
波 [pɔ] ball
波士 [pɔ si] boss
杯葛 [pui kɔt] boycott
班 [pan] band
甫士 [p'ou si] pose
派對 [p'at t'i] party
拍乸 [p'at na] partner
泊車 [p'ak ts'ɛ] park (a car)
媽咪 [ma mi] mammy
孖氈 [ma tsin] merchant
迷你 [mɐi nei] mini skirt
嘜 [mɐk] mark
花臣 [fa sɐn] fashion
科文 [fɔ mɐn] foreman
科騷 [fɔ sou] floor-show
快勞 [fai lou] file
肥佬 [fei lou] fail
咕喱 [ku lei] coolie
爹哋 [tɛ ti] daddy
多士 [tɔ si ]toast
T 恤 [t'i søt] shirt
貼士 [t'ip si] tips
乃昔 [nai sɩk] milk shake
鐳射 [løy sɛ] laser
啫喱 [tsɛ lei] jelly
知士 [tsi si] cheese
仄紙 [tsɐk tsi] cheque
士班拿(士巴拿)[sin pan na (si pa na)] spanner
士多 [si tɔ ] store
士多啤梨 [si tɔ pɛ lei] strawberry
摔 [søt] shoot
茄喱啡 [kɛ lɛ fɛ] care free
畸士(K 事) [k'ei si] case
咭 [k'it] kid
[X] [ts'ip] cheap
柯打 [ɔ ta] order
溫拿 [wɐn na] winner