Unicode for \trianglelefteqslant
This operator would be in the Mathematical Operators block (or its supplemental block), but it's not there, so the answer is simply
no
Maybe there exists a font which has this symbol in the private use area, but that doesn't count as Unicode.
I guess the point whether these symbols are in Unicode is rather secondary, unless you want to enter the literal Unicode symbol (which unfortunately does not exist). The fact whether they are accessible in LaTeX when using a Unicode math font is more important. The symbols in question are defined by the stmaryrd package, which works in conjunction with Unicode math. It is probably a good idea to load stmaryrd before unicode-math, such that unicode-math can overwrite symbols from stmaryrd, which actually are in Unicode.
\documentclass{article}
\usepackage{stmaryrd}
\usepackage{unicode-math}
\begin{document}
$\trianglelefteqslant \ntrianglelefteqslant$
\end{document}
it's true that these symbols aren't in unicode.
the simplest answer for why this is so is probably that no one requested them at the time when the mass addition of math symbols was happening. if they were recognized, it would almost certainly be with "variant selector 1" (VS1). see the table on pp.28-29 of unicode technical report #25 (can be viewed on the unicode site).
as presenter of the stix symbols collection for addition to unicode (and co-author of tech report #25), i still have contacts within the unicode technical committee, and can suggest that additional symbols be recognized. the VS1 route is almost certainly the approach to be taken, since there is no difference in meaning (that i'm aware of) between the symbol with a horizontal equality stroke and a slanted stroke.
henri menke's identification of the desired symbol in the stmaryrd font is currently the best solution, but a unicode equivalent is certainly desirable (even though it will probably cause trouble for the mathml maintainers). i believe there are some other symbols in stmaryrd that are also in the same unfortunate limbo.
i'm currently in the process of retiring from the ams, and won't be able to do anything useful for a couple of weeks, but i intend to follow up. if there are other similar symbol instances that can be presented at the same time, please identify them in comments, and i will submit all of them together.