I've tossed this into godbolt
On gcc (8.3) and clang (8.0.0) with -O3 optimizations, that function compiles into a no-op function. Impressively, this is even true for MSVC v19.20 with /O2 optimizations.
GCC 8.3 / Clang 8.0.0:
a(int):
        ret
MSVC v19.20 (x64):
i$ = 8
void a(int) PROC                               ; a, COMDAT
        ret     0
void a(int) ENDP                               ; a
I've also taken the liberty of making the example non-trivial. The code I'm using from here on is:
#include <iostream>
void a(int i)
{
    std::cout << "hello\n";
    if (i > 0)
        a(i - 1);
}
The compiler output for this with gcc trunc with -O3 optimizations enabled is the following:
.LC0:
        .string "hello\n"
a(int):
        push    rbx
        mov     ebx, edi
        jmp     .L3
.L6:
        sub     ebx, 1
.L3:
        mov     edx, 6
        mov     esi, OFFSET FLAT:.LC0
        mov     edi, OFFSET FLAT:_ZSt4cout
        call    std::basic_ostream<char, std::char_traits<char> >& std::__ostream_insert<char, std::char_traits<char> >(std::basic_ostream<char, std::char_traits<char> >&, char const*, long)
        test    ebx, ebx
        jg      .L6
        pop     rbx
        ret
_GLOBAL__sub_I_a(int):
        sub     rsp, 8
        mov     edi, OFFSET FLAT:_ZStL8__ioinit
        call    std::ios_base::Init::Init() [complete object constructor]
        mov     edx, OFFSET FLAT:__dso_handle
        mov     esi, OFFSET FLAT:_ZStL8__ioinit
        mov     edi, OFFSET FLAT:_ZNSt8ios_base4InitD1Ev
        add     rsp, 8
        jmp     __cxa_atexit
From careful examination, the only call instruction is to the io method to write the message on each iteration. A test is then performed (the if statement). If i > 0, control jumps up, decrements i and does it all again. The other branch of the if statement (false case) simply returns (after stack cleanup).
Thus, there is no buildup of stack frames even in this non-trivial example. It is performed via the jmp instruction because (as you said) the previous execution information is irrelevant.