It is absolutely essential to pronounce the vowel sounds accurately in order to be understood.
Thankfully, the vowel sounds in Thai are very consistent, they do not change depending on your region, as in English. There are regional dialects in Thailand, of course, but if you pronounce the vowels in particular the ‘standard’ (middle-country) way then you will be universally understood.
There are only nine vowel shapes in Thai. All the vowels are made up of short (cut-off) or long versions of these sounds, or of two vowel sounds pronounced in sequence (“dipthongs”).
Trying to learn to speak Thai using a phonetic transliteration scheme is doomed to failure. You will very likely end up mangling and mispronouncing Thai. Learn at least to recognize the Thai vowels and make sure to watch the following youtube videos and practice the shapes until they become a subconscious muscle memory...
Part 1
Part 2