I traveled for two months last fall on an RTW - US -> South Pacific -> Asia -> Gulf States -> Europe -> US
I used a dual SIM Samsung S7 Edge, with AT&T and T-Mobile SIM. I also had a separate GSM phone for a HK/China Telecom SIM I used for data roaming only in China.
The S7 has controls for each SIM, and whether each would roam or not for data. I had no inadvertent triggers of the AT&T day pass by having the phone default to the T-Mobile SIM for phone/text/data. I only enabled the AT&T SIM when I wished to use the day-pass.
I get a lot of texts from for banking and confirmations. Before departing the US, I made sure all of them used my Google Voice telephone number for text notifications. Within Google Voice, I can then configure which of my cell phone numbers or email addresses get text msgs forwarded to.
For certain people, I provided them with my Google Voice phone number to use if they needed to reach me. Again, I could control which cell phone number I would have Google Voice ring, when I wanted to.
The end result was no inadvertent voice/texts/data usage to trigger an AT&T International Day Pass unless I wanted to.
Also, be sure to understand in what countries the day pass is valid. There are exceptions. Also be aware that T-Mobile "free" text and data doesn't work in every country, either.
Free WiFi almost everywhere I went, so Google Voice was useful for receiving texts, calls, and voicemails when connected.
One unexpected surprise: When I activated my data SIM in China, and shared my hotspot with a few friends traveling with me, the data was consumed rather quickly. This was because my connected friends did not know how to turn off their background data usage. I had to change the password to knock them off.