if your manifest is set up correctly, your app can be
launched when an nfc tag is discovered. you don't
need something running in the background, even if
it were possible. and, therefore, your app doesn't
need to be running all the time when the tag is
discovered. it just needs to be launched, which
the system will do if your manifest is correct.
nfc discovery intent filters are activity filters. that
is, they launch an activity. and nfc handling must
be done in the foreground. with the applicable
intent filter, your app might be called to read the tag.
without the applicable intent filter, you app will not
be launched. but you might still be able to read the
tag if your app is already in the foreground.
if multiple apps have the same intent filter(s), the
user has to decide which gets launched (unless your
app is already in the foreground). note: just because
your app is in the foreground when the tag is detected
does not mean you will be able to read it. the tag may
support a technology not recognized by your app.
the tag you mention is mifare classic 1k compatible,
android can deal with it.