yes, if the fuse for the ABS blows, the 12v will not be present to bypass the spider.
here is one fix The Definitive Alarm Spider Post - LR4x4 - The Land Rover Forum
i was going to do this, which is what the previous owner already basically did by routing the harness through the ABS fuses.
AMR4956 IMMOBILISER CENTRE CONSOLE LOOM | Discovery 1 1989-1998: Accessories: Interior | shop | www.lrseries.com | L. R. Series
if you can't find the spider or the harness, eek. i had my entire dash apart before i figured it out.
good luck.