The original motivation for the
psnfss packages such as
times was to use the fonts built in to the new PostScript laser printers. So
times package selects (or at least selected) Adobe (licenced from Linotype) Times Roman. Apart from giving the look of Times Roman this had the distinct advantage at the time as the generated PostScript files were much smaller as they had no fonts embedded.
newtxtext package selects a Times Roman clone, TeX Gyre Termes.
Normally packages selecting different fonts would not be considered to be the same, or one deprecated in terms of the other.
The situation here is complicated though as (with no change to the TeX macros of the
times package) most TeX distributions now set the default map files for Times Roman to not use the built in Times Font but rather embed a Times clone (the Nimbus font originally donated by URW to the ghostscript project). The TeX Gyre Times Roman clone is also based on the glyphs in this URW font, so the differences between the fonts are not as large as they might be.
However to answer the question
Will anyone actually be able to tell if I use newtx, instead of times ?
Then yes depending how they look:
Depending which package is used, pdffonts info shows
PKIZXQ+TeXGyreTermes-Regular Type 1 Custom
VXPZSB+NimbusRomNo9L-Regu Type 1 Custom
If you just use
times package, then any mathematics will be set in the default computer modern and look very light in comparison, so the close cousin of the
mathptm(x) soon followed. Unlike the text case, the constraints of using virtual fonts to access fonts built in to a 1980's laser printer, plus fonts available in a 1980s tex distribution fonts mean that in comparison to later math fonts for TeX,
mathptm is rather, hmm basic (and
mathptmx only slightly less so). However you can not just switch an existing document to a different font setup as the metrics are different and all line and page breaking would change, so it would not be appropriate to withdraw these packages or even really make them give warnings, however for new documents
newtxmath will certainly give better math setting in general.
Is it worth writing to conference organizers asking the to amend their guidelines.
Possibly, possibly not. The organisers probably have other things to worry about. Also they may have some agreement with a publisher for the conference proceedings, so they may be constrained to whatever requirements they have for publishing (and publisher classes can be very strange:-)
So your next question
if so is there an authoritative statement (that is more substantial than the paragraph on CTAN) saying that it is deprecated and why?
Not really, ctan has lots of packages in lots of states of maintenance or lack of maintenance. The users need to determine if any packages they use are suitable for the use at hand, there is no review and no authority that can make such a statement.
Is it better to wait until after a conference has occurred that gave the time recommendation, then contact the organizers of the next year's conference?
As for the previous question, it may be worth mentioning it, but next years organisers might have the same internal constraints as this years.