“Is Linux Addictive…”
Only insomuch as freedom to compute the way you want without being tracked and trafficked is addictive. 
“(Specifically the Librem 5)”
That would be entirely up to you. Use it as you think appropriate.
EDIT: On my home network, Pi-hole indicates that my Librem 5 has connected to the following over the last 7 days:
<number>.debian.pool.ntp.org
<MyIPaddress>.in-addr.arpa
<numbers>.e.f.ip6.arpa
_https._tcp.repo.pureos.net
_sip._udp.<MyVoipProvider>.com
bravo<numbers>.<MyVoipProvider>.com
<MyVoipProvider>.com
_stun._udp.<MyXMPPprovider>
_xmpp-client._tcp.<MyXMPPprovider>
<MyXMPPprovider>
appstream.pureos.net
dl.flathub.org
location.services.mozilla.com
locprod2-elb-us-west-2.prod.mozaws.net
odrs.gnome.org
pureos.store
repo.pureos.net
whois.radb.net
P.S. Mainly just turning on and updating, backing up, connecting to WiFi and mobile network; not really spending time in any apps.