No experience in any 300s here...but here is the typical unhelpful government text from the TCDS that mentions both:
Certification Basis Special Federal Aviation Regulation (SFAR) 41C, effective September 13,
(Model 300, 300LW) 1982, see NOTE 7 or 11 (300 only); Part 23 of the Federal Aviation
Regulations (FARs), effective February 1, 1965, through Amendment 23-9;
Amendment 23-11; Amendment 23-14, Paragraphs 23.143(a), 23.145(d),
23.153, 23.161(c)(3), 23.173(a), 23.175, 23.427, 23.441, and 23.445;
Amendment 23-15, Paragraphs 23.951(c) and FAR 23.997(d); Amendment 23-23,
Paragraph 23.1545(a); Amendment 23-26, Paragraphs 23.967 and 23.1305(n);
Special Conditions No. 23-47-CE-5, including Amendments Nos. 1, 2, 3
dated November 15, 1982, and 4 dated October 17, 1986; Part 25 of the
FAR, Paragraph 25.929, effective February 1, 1965, Amendment 25-23,
Paragraph 25.1419; Amendment 25-41, Paragraph 25.831(d); Part 36 of
the FARs, through Amendment 36-10, and SFAR 27, through Amendment 27-4.
Compliance with ice protection has been demonstrated in accordance with
FAR 25.1419 when ice protection equipment is installed in accordance
with the Equipment List.
TCDS
However, here is a picture of a King Air 300 for sale with a Garmin 400 in it...so it's at least possible:
KingAir300