There is not any interaction. The maximum-paths command is used by the process that manages the active routing table and specifies how many Active Paths will be inserted into the routing table. According to the Cisco documentation BGP PIC Edge for IP and MPLS-VPN feature creates and stores a backup/alternate path in the routing information base (RIB), forwarding information base (FIB), and Cisco Express Forwarding so that when a failure is detected, the backup/alternate path can immediately take over, thus enabling fast failover. So PIC is dealing with backup path and not primary path. Here is the link if you want additional detail
https://www.cisco.com/c/en/us/td/docs/ios-xml/ios/iproute_bgp/configuration/xe-3s/irg-xe-3s-book/irg-bgp-mp-pic.html
HTH
Rick
HTH
Rick