AFAICT it depends on whether the bottleneck moves to the server's NIC, and if so, what the qdisc is for transmissions from that NIC.
If the server's NIC is faster than the sum of the demands of the apps, and faster than any potential bottleneck links in the network, then the bottleneck will not move to the server, and the fact that the flows are on the same server should not matter.
If the server's NIC is the bottleneck, then the server's qdisc will come into play. Hopefully the server is using a modern qdisc like fq_codel and fq, and that will enforce fairness explicitly. Even if it's using a pure FIFO qdisc, the flows should converge to fairness via some combination of TSQ and normal BBR sharing dynamics. (Again, if one flow is using less than its fair share, then that flow will only get what it tries to use, and the other flow will get whatever is left.)