1/ Is it possible: short answer, no.
There are edge cases, that would require for someone to create another Ingress object exposing Service2 in the first place. Then, you could trick the Ingress into routing you to some service that might not otherwise be reachable (if the DNS doesn't exist, some VIP was not yet exposed, ...)
There's no real issue with external clients bypassing the ELB, as long as they can not join all ports on your nodes, just the ones bound by your ingress controller.
2/ Bypassing the loadbalancer: won't change much in terms of performance.
If we're talking about a TCP loadbalancer, getting it away would help track real client IPs, though. Figuring out how to change it for an HTTP loadbalancer may be better -- though not always easy.
3/ Removing the LoadBalancer: if you have several nodes hosting replicas of your incress controller, then you would still be able to do some kind of DNS-based loadbalancing. Though for sure, it's not the same as having a real LB.
In AWS, you could find a middle ground setting up health-check based Route53 Records: set one for each node hosting an ingress controller, create another regrouping all healthy ingress nodes, then change your existing ingress FQDN records so they'ld all point to your new route53 name. You'ld be able to do TCP/HTTP checks against EC2 instances IPs, that's usually good enough. But again: DNS loadbalancing can suffer from outdated browser caches, some ISP not refreshing zones, ... LB is the real thing.
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