The Thai vowel อู is a high, back, rounded vowel.
The corresponding Lao vowel is very similar and for the Khmer one I can’t comment.
The first element of the Vietnamese diphthong in mười is the vowel ư,
which is a high, central, unrounded vowel.
Vietnamese also has a vowel u, which is like อู is a high back rounded vowel.
The vowel ư in mười is essentially different from อู in that it is unrounded.
If anything, u would correspond to อู instead.
Long answer (based on short answer)
The sample formant values shown in the below paint, indicate a slightly more complex picture:
อู u ư
F1 1417.62 470 380
F2 918.76 760 1390
F3 2776.98 2690 2870
These values put อู somewhere between ư, and u, though quite a bit closer to u.
I think it's still fair to say that there is an essential difference between อู and ư, in that one is rounded and the other is not.
The take-away is really that อู is not exactly the same as u either.
On a practical level, if you use it in place of ư, it is likely to be heard as u, or at the very least, you will have a hard time making a distinction between ư and u.
Sources of the formant values (and the qualitative descriptions of the vowels):
Thai: Directly reported in Narang and Misra, Acoustic Space, Duration and Formant Patterns in vowels of Bangkok Thai, Language Processing 20(3) 123.
Vietnamese: Via Praat from the native-speaker examples in the pronunciation guide in Bin Nhu Ngo, Elementary Vietnamese, Tuttle 2015 (based on Hanoi Vietnamese).