I agree with the OP. It happens a lot in connected speech.
Whenever a word ends in /ʊ/, /u/ or a diphthong that ends in /ʊ/, /aʊ/, /əʊ/, /oʊ/ etc., native English speakers often end that word with a /w/. It mostly happens when one word ends with either of the above vowels and the next word starts with a vowel.
go away -> [ɡəʊ][w][əweɪ]
go on -> [ɡəʊ][w][ɒn]
now and.. -> [naʊ][w][ənd] etc.
Whenever a word ends with a front vowel /i/, /ɪ/ or a diphthong that ends in /ɪ/ /aɪ/, /ɔɪ/ etc., native speakers are more likely to end it with a /j/ (the 'y' sound as in yes).
I agree -> [aɪ][j][əɡriː]
See it -> [siː][j][ɪt] etc.
There's also an intrusive R. When one word ends with /ɔ/ (and some other vowels like /ə/, /ɪə/ and /ɑː/) and another word starts with a vowel, there's often an intrusive R between both the words. So for example native speakers often pronounce saw it [sɔː][r][ɪt]. It's more common in non-rhotic accents than in rhotic accents.
There's no 'correct' or 'incorrect'. Pronounce it however you want.
However, if it's difficult for you to pronounce it with the intrusive consonants, you can pronounce the second word with a glottal stop. So you'll also hear go away being pronounced [ɡəʊ][ʔ][əweɪ], but pronouncing it with a /w/ sounds more natural.
(It's been explained in this answer.)