In a word, "no" :-)
Linux tar will not stop any other process from reading the files while it is running.
If you are concerned about writing the tar doesn't block that either, but if a file changes while tar is reading it then you'll get a warning message; if the directory structure changes while tar is in the middle of it then you might see some oddities in the results (missing files, duplicated files on both paths, etc).
So reads are perfectly safe, writes may require a little more care.