How to determine the input resistance of a bootstrapped emitter follower
Well, the equation for the Zin and voltage gain looks for the emitter follower with the bootstrap (positive feedback) at the input







simulate this circuit &ndash; Schematic created using CircuitLab

looks like this: 

$$Z_{IN} = \frac{(r_eR_E + R_3(r_e + R_E))\cdot (1 + \beta)}{R_3 + (\beta+1)r_e }\approx \frac{R_3}{1 - A_V}||(r_e+R_E)(\beta+1)$$

$$A_V = \frac{(R_3+r_e) R_E}{r_e R_E + R_3r_e + R_3R_E} = \frac{R_E}{R_3||r_e + R_E} \approx \frac{R_E}{r_e+R_E}$$

Of course \$R_E\$ is for your circuit equal to

$$R_E = R1||R2||R4$$ 

So, in conclusion, your reasoning is correct