This is doable, but unrealistic. It will take forever and numerous SMS texts (or even numerous 300KB MMS texts). I started a trial to figure out some numbers. And here is what I found out..
With a 35KB file (smallest, reasonably sized file I had on my phone other than a .txt file):
~5 minutes to process.
~640 SMS texts
~0.3 MMS texts
That means for a 300KB file (the smallest max MMS size for carriers):
~43 minutes to process
~5,490 SMS texts
~2.5 MMS texts
And for a 1.21MB file (my 5MP camera file size):
~22,700 SMS texts
~10 MMS texts
The reason it takes so long, is once you use the filestream to read into a byte array. You have to append the byte array values into a string for sending ("23,162,5,93,239" instead of B). Using a simple for loop, this takes about half a millisecond, but it adds up for each byte in the array when there are thousands of bytes.
For average sized files, it would be pointless to send 2-3 MMS when it can fit in one MMS file although you could send any file type. But when you try to send a large picture without resizing, the fact that it would take 3 hours to compile is a bust. Unless I'm missing a way to send a byte array or a faster way to compile it to a string..