Can a 4L80E swap be tuned in HP Tuners by just selecting 4L80E in the trans type menu, without doing a segment swap?

Here is what the documentation says. Each point links to its source; details depend on your exact computer, harness and transmission.

Transmission control

• When changing transmission type with HP Tuners, select a donor operating system from a similar vehicle that originally came equipped with the desired transmission. (HP Tuners)
• HP Tuners' official Segment Swapper procedure imports both the diagnostic data segment and the transmission data segment from the donor file into the current calibration. (HP Tuners)
• The official HP Tuners walkthrough uses a 2000 Chevrolet Tahoe 5.3/4L60E converted to a 4L80E as its example application. (HP Tuners)
• After the swap, save the calibration under a new filename, reopen it, and confirm it reflects the new transmission type and related settings before writing. (HP Tuners)
• The final step of the official procedure is to write the entire new calibration back to the vehicle's control module. (HP Tuners)

Other wiring

• P01/P59; Vortec LS; 4L60E to 4L80E; 1999-2007: Converting a Painless Vortec harness transmission connector from 4L60E to 4L80E requires moving the brown wire from terminal location U into terminal location S; the white wire has no function with the 4L80E and is taped up and stowed. (Painless Performance Products (via Scribd mirror))

Confirm against the instructions for your exact parts before wiring. More: Transmission control in our tuning guide.