What happens if I ask 127.0.0.1 via arp broadcasting?

Nobody should answer your request, because every network interface should only answer for addresses bound to them (i.e. not for other interfaces).

Linux boxes may respond.

http://lwn.net/Articles/45373/

"If a Linux system (with a default configuration) receives an ARP request on one of its interfaces, and that request is looking for an IP address assigned to any of the systems interfaces, the system will respond to the ARP request through the interface that received it. This response happens even if the interface involved is not the one to which the requested address has been assigned."

This depends on how well-written (or buggy) the responding TCP/IP stacks are.

You shouldn't get any responses, but I've seen bizarre behavior before too...

Given that RFC1122 (Requirements for Internet Hosts) states for the 127/8 address block:

Addresses of this form MUST NOT appear outside a host.

And RFC1812 (Requirements for IP Version 4 Routers) states:

  A router SHOULD NOT forward, except over a loopback interface, any
  packet that has a destination address on network 127.  A router
  MAY have a switch that allows the network manager to disable these
  checks.  If such a switch is provided, it MUST default to
  performing the checks.

The obvious question is why would you ever ARP for 127.0.0.1 if you are not meant to send packets to those addresses over anything other than loopback interfaces?

From your original question:

"Will all computers on the network answer me?" - No.

"What will happen?" - results will vary from nothing at all happening to getting responses from isolated hosts/gateways that are likely buggy or misconfigured.