If you have Data Roaming turned off, you won't be able to access the internet at all over the cellphone network whilst not connected to the network your SIM is designed for.
Having Data Roaming turned off will have no effect if you are connected directly to your SIMs cell network in your Home country.
If you turn off "Cellular Data" you won't be able to access the internet at all, regardless of which cell network you are connected to.
Would there be any adverse affect to my bill if I have "cellular data" on while outside of the US?
If you have Cellular Data turned "on" whilst outside the US, but Data Roaming "off", then you still won't be able to access the internet as the Data Roaming "off" setting would override the Cellular Data "on" setting.
See:
http://support.apple.com/kb/HT4203