Yes, it should stay up. You have to shutdown the service before running make install, which is essentially the step that copies the binaries/build. Generally, make install takes about 1-2 minutes so do plan for a brief httpd outage.
The php recompilation will not affect the normal working of webserver. After you recompile the php the new binary is created or .so file is overwritten. The new php will be only taken when you restart the webserver. When you restart the webserver configuration and the resultant binaries are stored into the memory space. During another restart the new values are stored into the memory space.