Yes, that will install the latest version of GMP in /usr/local. However, you then need to use some special flags to link against it. Here's a snippet from my Linux compilation guide which modifies makefile.unix.
cp makefile.unix makefile.my
sed -i -e 's/$(OPENSSL_INCLUDE_PATH))/$(OPENSSL_INCLUDE_PATH) \/usr\/local\/include)/' makefile.my
sed -i -e 's/$(OPENSSL_LIB_PATH))/$(OPENSSL_LIB_PATH) \/usr\/local\/lib)/' makefile.my
sed -i -e 's/$(LDHARDENING) $(LDFLAGS)/$(LDHARDENING) -Wl,-rpath,\/usr\/local\/lib $(LDFLAGS)/' makefile.my
After that run "make -f makefile.my clean" and then "make -f makefile.my".
Also, it's possible to check that you're using your own custom libgmp by typing "ldd primecoind". The output should say something like this:
libgmp.so.10 => /usr/local/lib/libgmp.so.10 (0x0000003822600000)
That means it's using the libgmp installed in /usr/local.