If i will not apply the egress-policy will the conexion still work, will there be log messages ?
Please define what do You mean by "conexion" (presumably "connection").
If You mean TCP session towards this shared address then yes, it will work but the TCP client won't get to choose where it is connecting to: it will be always connecting to the closest node with that anycast IP.
The best practice is to have 2 IP addresses on lo0.0: one unique which also serves as router-id, and second shared/anycast, which is only redistributed into IGP since MPLS anycast is quite rare technology and really is developed in the context of Segment Routing.
If You have a mixed network with CSCO routers, then JUNOS egress policy is pretty much required to avoid the messages cited in CSCO support forums link.