There's no "risk" in terms of costs.
If you didn't already pay for plan or add-ons which provision data then you can't use data and you won't be charged for data. At PM there's never any overcharges, you pre-pay for the (data) service or you don't get provisioned for the service.
If you didn't already pay for plan or add-ons which have USA roaming then you won't get USA roaming and you won't be charged for USA roaming. Even if you (your phone) is in USA and pinging American towers.
There is "risk" in terms of cellular radio traffic - it can be intercepted or monitored by anyone with technical (and presumably legal) ability to eavesdrop on the signals. Same as with any other phone on any other carrier. This risk is never zero but it's basically insignificant when you're not actually using your phone to talk or msg or send logins across data.
It's theoretically possible for wireless hackers ("whackers") to capture or spoof the SIM ID and IMEI from any device connected to the network, but again the non-zero risk is basically insignificant. Few criminals would have the necessary tech savvy, equipment, and patience to accomplish this.
It's definitely possible for your (your phone's) location and movements to be tracked through simple radiolocation. Even without a SIM card. The only way to mitigate this risk is Airplane Mode - or better yet, turn the phone off and remove battery.
Excessive radio transmission (like searching networks) does drain battery fairly quickly. Airplane Mode prevents this. Or at least it's supposed to - power off and remove battery if you're a tinfoil hat kinda person.
Standard Android (and iOS) won't allow cellular networks to be disabled if a SIM card is installed (even if the SIM isn't valid). Non-standard operating systems (like GrapheneOS and CyanogenMod) could offer this feature, or instead could allow the phone's built-in apps to be replaced by apps which offer user control over this default behaviour. Assuming the device model has been fully reverse-engineered and there's no need to rely on proprietary embedded "black box" code blobs.
