Can I leave the country while pending for change of status from H1b to H4?

Are you sure you are not confusing visa with status? If you change your status you will need to get the appropriate visa stamped in your passport in order to be admitted into US. Note that the US consulate may not look favorable at your modus operandi, therefore consult an experienced immigration attorney before you make any step in the wrong direction.

You could, but would be abandoning the COS request in the process.

If you must travel for a family emergency, or such then you can travel. Departing while an extension of stay/change of status petition is pending may lead to a finding of abandonment. However, this will have little to no impact on your immigration history. Just keep a copy of the notice you may receive from USICS stating that you abandoned your application as of the date of departure. If you want to be extra cautious you can have a letter written requesting the exact dates you will be departing and request your H-4 be valid until that date. Also, if you depart the US, you will need to obtain an H-4 stamp in your passport (if you do not already have one) to return to the US on H-4 status.