Yes, lab-created diamonds will test positive as diamonds on most diamond testers because they have the same physical and chemical properties as natural diamonds. Diamond testers typically rely on thermal conductivity to distinguish diamonds from other materials, and both natural and lab-created diamonds have a high thermal conductivity that is different from most other materials.
However, it's worth noting that there are some advanced detection methods that can distinguish lab-created diamonds from natural diamonds, such as spectroscopy or UV fluorescence testing. This may be important in some contexts, such as in the diamond trade where natural diamonds typically command a higher price than lab-created diamonds. But for most purposes, such as jewelry or personal use, a standard diamond tester should be sufficient to confirm that a lab-created diamond is indeed a diamond.