This is good yellowcloud. Although where possible, 'support indefinitely', if it can be reasonably proven, supersedes 'support for xx weeks'.
Your ESA is not a public fund also because it is a means to faciliate you to live normally, so beyond Immigration Rules, you have an inalieable right to use this money as you see fit to live a 'normal life', which includes getting married [and you can't be refused the right to marry under International human rights convention simply because you are disabled - as no individual can be told by the state when they can or cannot marry and start a family, nor can the state lawfully hinder you from doing so - ESA helps not hinders therefore... You get the idea I'm sure! A lawyer will regard this as a politico-legal argument and not a purely legal one, but it still applies in law].
So go ahead and roll the dice if you got your housing issue sorted.
