No cucumbers do not continue to ripen once they're picked off the vine like some other fruits do.
So you have to wait for the cucumbers to fully ripen when growing on the vine before picking the cucumbers because once picked off the vine the cucumbers will not ripen anymore.
When cucumbers are fully ripened on the vine the cucumbers flesh will be green and firm and if the flesh is not firm and green the cucumbers need to grow a little longer before picking them.