So it should work if I replace the variable capacitor with a varacap assembly with a red LED in the place of the varacap?It would be tricky to bias a varicap - you'd have to stabilise the decoupled collector rail.
If the decoupled rail is "tight" enough - you might be able to get away with grounding one end of the varicap.
The inductor will obviously shunt any DC for a varicap, you have to DC block it with a series capacitor big enough to have little effect on the total capacitance. The varicap is used reversed biased, so there's only a tiny leakage current - you can feed it with a high resistance that doesn't clobber Q very much.
Pedantic theorists will tell you that the RF which is an AC waveform, will sum with the varicap bias and degrade tuning accuracy - millions of TV tuners don't worry about it and work just fine. High end FM tuners sometimes have twin or double ended varicaps which cancel out the AC offset.