This is generally a very poor way to learn a language.
Aside from the obvious, that the student won't know how to read or write after learning this way, they probably won't learn to speak very well, either.
Transcribing one language to another, as a way of pronunciation training, is generally a very bad idea, for the simple reason that no two languages have identical phonology.
A cursory examination of Tamil phonology and English phonology reveals that the languages (nearly*) share the following consonants:
While these are found only in English:
- b
- f
- v
- θ
- ð
- t
- d
- s
- z
- ɹ
- t͡ʃ
- d͡ʒ
- ʃ
- ʒ
- ɡ
- x
- w
And these vowels (not differentiating for long and short variants):
With these being found only in English:
From this over-simplified view of the two languages, Tamil only has 31% of English's phenoms. This means that, in a best-case scenario, a student learning to speak English by reading Tamil script will, in a best-case scenario, be learning 69% of the sound incorrectly. (Note this does not account for the relative frequency of any of the phenoms.)
As a more concrete example, I took your sample phrase, "My name is Kolappan", and piped it through espeak to get the the IPA transcription in English:
ma͡ɪ ne͡ɪm ɪz ˈkɑːlɐˌpæn
I then did the same for your transcription "மை நேம் இச் கோலப்பன்", and I got:
ma͡ɪ neːm ˈit͡ʃ ˈkoːlʌppʌn
Now it's important to note that espeak's IPA transcriptions aren't always accurate, especially for certain languages, and its output is fine-tuned for its own speech algorithm, not for "proper" IPA output, but even so, you can see some distinct differences between the transcriptions:
ma͡ɪ ne͡ɪm ɪz ˈkɑːlɐˌpæn
ma͡ɪ neːm it͡ʃ ˈkoːlʌppʌn
With 14 distinct phenoms, only 8 are the same, or 57%, in this example. And some of the differences are incredibly distinct. For instance, pronouncing [it͡ʃ] instead of [ɪz], is likely to be frequently misunderstood. And the pronunciation of the name is drastically different, as well.
So in summary: Transcription into one's native alphabet is a pretty poor way to learn a new language. If the goal is to avoid learning to read and write, a student would be much better of learning a new language by speaking and listening, without the use of transcription.
*Even when the IPA symbol for sounds between two languages is identical, it doesn't necessarily mean the pronunciation between them is identical. And the variation gets even more complex when you account for different dialects.