No, the fitness tracker cannot tell that exercise has changed. This will result in a skewed value.
Fitness trackers usually look at your age, weight, sex, heart rate, overall fitness level, and effort to determine a VO2max estimate. The way that effort is calculated is by examining your heart rate compared to the exercise type. So, if you tell the fitness tracker you're walking and your heart rate goes up because you're actually running, your effort goes up, and your VO2max would go down (GPS mitigates this to an extent; a better example might be walking vs walking in snow). Garmin themselves gives three good scenarios to estimate your VO2max and they are fairly rigid (i.e. strictly walking/running/cycling, at a steady pace, for greater than 10 minutes).
"Cycling VO2 Max Tip: If you are having difficulty obtaining a cycling VO2 Max Estimate, try riding a course where you can maintain a steady effort. You can also try using an indoor trainer."
Aside from that, a lot of VO2max computation and fitness tracker coding is proprietary. It is good to keep in mind that these are estimates regardless of the price of the fitness tracker.