You're mixing up your ethernet layer and your IP layer.
Remember that ARP is a protocol where a host broadcasts "who has IP address x?" on a given ethernet, and (usually) receives an answer from that host in the form "x is on ethernet address X". Additionally, to save time, when they bring up an interface, most hosts will send out "gratuitous ARP" and say "I am here", to refresh the caches of locally connected devices.
Here is your situation with your routers relabelled for clarity.
R1 has three interfaces each with an ethernet address A, B, C to which hve been given three IP addresses, a, b, c (perhaps 10.0.1.1, 10.0.2.1, 10.0.3.1)
R2 has two interfaces with ethernet address D and E, and IP addresses d and e (10.0.1.2 and 10.1.0.1)
R3 has two interfaces with ethernet address F and G, and IP addresses f and g (10.0.2.2 and 10.2.0.1)
R4 has two interfaces with ethernet address H and I, and IP addresses h and i (10.0.3.2 and 10.3.0.1)
PC1 has ethernet address P and IP address p (10.1.0.99)
PC2 has ethernet address Q and IP address q (10.2.0.99)
a/ b| c\
/ | \
d/ f| h\
R2 R3 R4
When a packet goes from PC1 to PC2, the sequence is:
- PC1's routing table says "send all to default gateway" which is configured to be e.
- PC1 sends ARP for e; R2 answers with E.
- PC1 sends the packet with source IP address p, destination IP address q, wrapped in an ethernet frame with source P and destination E, the ethernet address of R2. Note that while the destination IP address is to the actual recipient, the destination ethernet address is to the nearside of the next hop. This is usually the source of any confusion
- Packet is received by R2, whose routing table says q is reached via R1 on a.
- R2 sends ARP for a; R1 answers with A.
- R2 sends the packet with the same IP addresses as previously, but in an ethernet frame with source B and destination F.
- R3 repeats the process, sees that q is on a local network, and sends ARP for q, PC2 answers with Q.
- R3 sends packet with the same IP addresses as previously, but in an ethernet frame with source G and destination Q.
That's all the case when everything is connected as described. If you unplug PC2 from that network and put it into the bottom of R3 without changing its IP address, then everything will be the same up to step 7.
Don't ask "will it try" something. Ask instead: What do the rules make each device do?
- R3 repeats the process, sees that q is on a local network, and sends ARP for q, but PC2 doesn't answer because it's not there.
- R3 will time out and give up on this packet. It might send a ICMP Destination Unreachable back to PC1.
The summary is that nothing will ARP for an IP address it doesn't think is local to one of its networks.
PS. There are obscure "proxy ARP" setups which don't work like this, but I haven't seen one since the last century.