Yes, but the distance will not be calculated correctly.
The pedometer has a mechanism to detect an up and down movement and record it as a step. This takes place regardless of the stride length.
Distance = number of steps x stride length.
There can only be one stride length, so if you walk some steps and run some steps, the distance will not be properly calculated. It is impossible for any device to know your true distance without GPS capability.
The important thing is that your step count will be calculated properly, assuming that your sports steps are still distinct steps and not shuffles. Thus, diverse activities such as cooking in the kitchen, playing tennis and moonwalking may not register all of the steps.
Additionally, you must walk at least 7 seconds in order for all of your steps to be counted. If you walk less than 7 seconds, none of those steps will be counted. If you walk at least 7 seconds, all of your steps, including the ones taken during the first 7 seconds, are counted.