link local address is used for ARP
Not sure what is your definition of link Local here - as per standard 169.254.0.0/16 is used for link-local purposes. this stays inside PC only.
When host is powered on with no internet
Can any body explain me how the IP allocation
ARP operations GARP
If the host is powered on and connected to the Switch port and you have DHCP, you get IP allocation from DHCP Server, does not matter whether you have an internet connection or not. and this IP can be reachable inside the Lan segment.
Gratuitous Address Resolution Protocol (GARP) requests provide duplicate IP address detection - this in short, RFC and google give you more example and use case.