Is this transfer function impossible with a low-pass Sallen-key filter?
Start with a 2nd order low pass filter transfer function in its general form: -

$$H(s) = \dfrac{\omega_n^2}{s^2 + 2\zeta\omega_ns + \omega_n^2}$$

And then mulitply this with a single order low pass filter transfer function: -

$$\dfrac{\omega_n}{s+\omega_n}$$

Giving you this: -

$$\dfrac{\omega_n}{s+\omega_n}\cdot \dfrac{\omega_n^2}{s^2 + 2\zeta\omega_ns + \omega_n^2}$$

Can you see that this is the same form as your equation and therefore, \$2\zeta\omega_n\$ must equal \$\omega_n\$ or put differently, \$\zeta\$ = 0.5.

The problem you have in your analysis is that you haven't factored-in the effect of zeta (\$\zeta\$) and a sallen key filter can quite often have a zeta below 1 because this can optimize the transfer function. Look up butterworth sallen key filters for example.