Yes and Yes; As long as you are rated for the category, class, and type (if required) of the aircraft that you are receiving the training in you could log both PIC and dual received.
14 CFR 61.51(e)(i) covers the logging of PIC time (which is perfectly legal in the scenario that you describe if you are rated in the aircraft):
§61.51 Pilot logbooks.
(e) Logging pilot-in-command flight time. (1) A sport, recreational,
private, commercial, or airline transport pilot may log pilot in
command flight time for flights-
(i) When the pilot is the sole manipulator of the controls of an
aircraft for which the pilot is rated, or has sport pilot privileges
for that category and class of aircraft, if the aircraft class rating
Training time is logged per 14 CFR 61.51(h) and you can log that too:
(h) Logging training time. (1) A person may log training time when
that person receives training from an authorized instructor in an
aircraft, flight simulator, or flight training device.
That being said, you may not act as the actual PIC however:
§61.31 Type rating requirements, additional training, and
(i) Additional training required for operating tailwheel airplanes.
(1) Except as provided in paragraph (i)(2) of this section, no person
may act as pilot in command of a tailwheel airplane unless that person
has received and logged flight training from an authorized instructor
in a tailwheel airplane and received an endorsement in the person's
logbook from an authorized instructor who found the person proficient
in the operation of a tailwheel airplane. The flight training must
include at least the following maneuvers and procedures:
Notice that the regulations governing acting as PIC are different than those governing logging of PIC time. This was done intentionally because there were so many pilots that were hired as SIC's at airlines with little to no PIC time and flew for years. When it was time for them to upgrade they didn't have enough PIC time even though they had lots of experience and could easily upgrade safely.