The LSL Products TLS-OEM Ultra Trik L Start 5 Amp Starting Battery Charger Maintainer - No Battery Clips will not drain the house batteries as it does not get the charge from the house batteries. The charge comes from stealing DC power from your house battery charger. Pulling the charge from the charging system it will keep your engine starting battery fully charged. Here is a copy of the manual
that also explains even more how this works.