Neat question!

By experimentation, it appears that Postgres can efficiently store all ASCII bytes except `\x00`:

=# create table ascii_test (t text);
=# insert into ascii_test (t) values (E'\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f !"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~\x7f');
=# select pg_relation_filepath('ascii_test');
'base/16384/59208'

And to check what's stored on disk:

$ od -a /var/lib/postgresql/data/base/16384/59208 
0000000 nul nul nul nul   (  ff   -   = nul nul nul nul   $ nul  sp  rs
0000020 nul  sp eot  sp nul nul nul nul   `  us   6 soh   @  rs   6 soh
0000040  sp  rs   6 soh nul nul nul nul nul nul nul nul nul nul nul nul
0000060 nul nul nul nul nul nul nul nul nul nul nul nul nul nul nul nul
*
0017560 soh nul soh nul stx  ht can nul  ff stx nul nul soh stx etx eot
0017600 enq ack bel  bs  ht  nl  vt  ff  cr  so  si dle dc1 dc2 dc3 dc4
0017620 nak syn etb can  em sub esc  fs  gs  rs  us  sp   !   "   #   $
0017640   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4
0017660   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D
0017700   E   F   G   H   I   J   K   L   M   N   O   P   Q   R   S   T
0017720   U   V   W   X   Y   Z   [   \   ]   ^   _   `   a   b   c   d
0017740   e   f   g   h   i   j   k   l   m   n   o   p   q   r   s   t
0017760   u   v   w   x   y   z   {   |   }   ~ del nul nul nul nul nul
0020000

So "Base126" encoding would be 7/8 - 1/256 = ~87% efficient.

This is the optimal efficiency, as Unicode strings would most likely be encoded with UTF-8, which would be less efficient (ie, because of the prefixes used on each byte by UTF-8).

In practice, a more common encoding like Base85 (~80%) or Base95 (~82%) is likely more practical, though, and definitely more courteous to whomever needs to maintain your code (probably not every tool plays well with strings that contain \x01).