Why not, though?
They're obviously at least partially physical constructs objects given that Shiro could get an arm graft from future Shiro and the magical circuit lineups were a plot point.
Then you have the worms, crests which can be transplanted despite being bunches of magic circuits, Rin transferring her magic crest to Shirou that one time, pedobait Jack's Surgical Procedure is implied to be at least partially mundane, and spiritual surgery can manipulate them too. I'm sure there's several other examples I'm missing, as well.
On top of that, it says explicitly that Rasputin's internal furnace allows him to integrate materials he swallows into his body. That seems like a sufficient loophole to be able to jack magic circuits. You did say Fate was all about loopholes, didn't you?

I'll accept getting nothing from bird because I misunderstood how familiars work apparently but I would argue that the theory is still sound.