Yes. Sinhala is not as close as Kannada script to Telugu but some letters do
bear a striking resemblance. There is a script called 'Old Peguan' somewhere
in Burma. Believe it or not, it bears almost as much resemblance to Telugu
as Kannada. If you want to check out try a book called 'Sign, Symbol,
and Script'. Unfortunately, I forgot the author's name. If anybody is keen
I can probably dig out the reference.
At the time of Nagarjuna, Telugu script didn't exist. Brahmi script was used
throughout India. There might have been close relationship even between Andhra
and Sinhala during even 10th or 11th century. Some scholars speculate that
Nannaya translated mahabharata into to cut down the influence of Budhdhism and
Jainism. A close inspection of the inscriptions will probably tell.