You can certainly prototype SMD parts in solderless breadboards and/or proto board using SMD adapters. Whilst I haven't seen an adapter for the X2SON package, there are many for the SOT23 - and you can even using stripboard or one-hole-per-pad for that. As far as I am aware - the devices are identical in behaviour, so you can just prototype with the easier SOT23.
The datasheet mentions both hysteresis - to prevent stuttering output when its close to threshold, and "ignores fast transients". But I assume you're worried that your application draws enough current to cause the power supply voltage to drop more than the hysteresis of the supervisor chip, and long enough to trip the reset - effectively causing it to "hiccup" - so it resets, powers up, draws more power, causes a reset etc..
The datasheet mensions there is 200ms delay between the supply voltage dropping below threshold, and the reset line going low so depending on the power up time of your micro that will at least prevent fast oscillation. Also, most microcontrollers have the facility to determine what caused the reset - whether internal brownout, or external reset pin. So perhaps you should include that in your firmware so it can check whether it was reset by a low battery, and take action - such as measure battery voltage, power back down, warn user, or prevent other peripherals from running.