Does "strictly conforming program" + no extensions == no diagnostics emitted?
No.
The only things for which the language specification requires diagnostics to be emitted are invalid syntax and constraint violations:
A conforming implementation shall produce at least one diagnostic
message (identified in an implementation-defined manner) if a
preprocessing translation unit or translation unit contains a
violation of any syntax rule or constraint, even if the behavior is
also explicitly specified as undefined or implementation-defined.
Diagnostic messages need not be produced in other circumstances.
(C2017, 5.1.1.3/1; emphasis added)
By definition, a strictly conforming program exhibits only valid syntax and does not contain any constraint violations, therefore the specification does not require a conforming implementation to emit any diagnostics when presented with such a program.
HOWEVER, the specification does not forbid implementations to emit diagnostics other than those that are required, and most implementations do, under some circumstances, emit diagnostics that are not required. The specification allows this, as clarified by footnote 9, which says, in part:
Of course, an
implementation is free to produce any number of diagnostics as long as
a valid program is still correctly translated.
Note also that "'strictly conforming program' + no extensions" is redundant. A program that makes use of any language extensions may conform, but it does not strictly conform:
A strictly conforming program shall use only those features of the
language and library specified in this International Standard. It
shall not produce output dependent on any unspecified, undefined,or
implementation-defined behavior, and shall not exceed any minimum
implementation limit.
(C2017 4/5; emphasis added)