Generally, nickel will be extremely low-resistance... ...like, on the order of 10 times lower than the nichrome equivalent. If it's a good sized coil under or just barely approaching .1, then it's definitely nickel. If you can fire it in power mode, then compare the resistance at room temp to the resistance after firing. It's gonna jump quite a lot if it's nickel. Nichrome, not so much, if at all. Maybe +/- .05-.1 ohms.
Anyway... ...yes, you can clapton non-tc wire around nickel. I've always done it that way because plain nickel doesn't do it for me. It has no oomf and one-note flavor imo. Plus, it allows you to do what is essentially a contact coil without having your readings all messed up or frying the wire.
It will still read correctly enough to work (sometimes a negligible amount higher, but usually the same as bare.) Realistically, the outer wrap has such a high resistance compared to the super-conductive core that 98% of the current is gonna go straight to the nickel core, anyway. We're talking double-digit ohms for the outer, so at vaping voltages, it's extra hundredths to thousandths of a watt per volt with that outer wire. Low enough to be considered non-conductive. If it was pulling significant power, you would see the resistance lower (such as with twisted or parallel.) Instead, it may increase by a just barely measurable amount because the outer wrap weakens the connection inside the post.
TC works by comparing the room temperature resistance against the operating one. It follows the TCR curve of the nickel, which increases linearly... ...as in, regardless of the starting resistance, it always increases at the same rate. So even if the resistance is higher than a nickel wire of that length usually would be, it still follows the same resistance curve. The numbers get shifted up in step with the base resistance. The kanthal makes no difference - it just slows the heating down.