In general yes it does, provided the favorable condition for hydrates to form.
Oil lines can get plugged similar to the gas lines due to hydrates if no preventive measures are taken.
However, some of the crude oils (e.g. Troika oil) contain natural surfactants which arguably act as hydrate anti-agglomerates preventing plugging.
Untill there is a clear understanding of such oil natural surfactants it is better to have preventive measures for hydrate formation in oil lines.