Does Brambleclaw become Squirrelpaw's mate

Yes they will but they do not have kits. Brambleclaw thinks Squirrelflight has Hollykit, Jaykit, and Lionkit but Squirrelflight was just keeping a secret for her sister, Leafpool. Those kits are actually Leafpool and Crowfeather's kits. Leafpool is the medicine cat so she is not allowed to have kits but she did.