Output length of an IIR Filter

In general, the output length of an FIR filter is given by (N+M-1) samples, where N stands for signal length and M stands for the number of filter coefficients. Can the same formulae be applied for IIR Filters? Let's say I have 4 input samples, 3 feed-forward coefficients, and 2 feedback coefficients. Then can I tell that my output length is 4+(3+2)-1? It is also known that the impulse response of an IIR Filter is not of finite duration. Does this thing affect the output length of an IIR filter, in any way?

$$y[n]=ay[n-1]+x[n]\tag{1}$$
You can verify yourself that for the specific input sequence $$x[n]=\delta[n]-a\delta[n-1]$$, the output sequence is finite and simply equals $$y[n]=\delta[n]$$. However, note that the use of finite precision arithmetic in an actual implementation may still result in non-zero output samples, even in cases when ideally the output samples should cancel.