At the time of this writing (July of 2021): no. Although a basic set of Egyptian hieroglyphic characters has been encoded in the Unicode Standard and a few fonts exist that contain these characters, current text processing software – whether word processor or page layout application or web browser – is unable to render the script adequately. It is true that users may insert Egyptian hieroglyphs as textual phrases, encoded with Unicode characters (at least as regards the basic Gardiner set of hieroglyphs) – and this is a great step forward. But proper shaping of hieroglyph text runs, like combining glyphs in quadrats, or reversing direction and mirroring, is not supported by any mainstream word processor such as MS Word, or page layout applications such as Adobe InDesign. On the other hand, using bitmapped pictures of hieroglyphs (.jpg, .png) leads to an unsatisfactory result.
The solution is to use a utility to do the correct shaping/ordering of the hieroglyphs, an application which can also produce resolution-independent illustrations to be inserted in a page layout application. The pre-eminent utility to do just that is JSesh, which also happens to be Open Source and free. It is available for MS Windows, macOS and various .nixes. JSesh produces excellent results. See also Submitting Egyptian hieroglyphs as images.
When the exact placement of Egyptian hieroglyphs is irrelevant and only single hieroglyphs need to be displayed (for instance in a sentence such as: “the phonetic value of 𓅓 as a ‘uniliteral sign’ is /m/”), the font Aegyptus Bold should be used (version 6.17 from 2017; this is the last version of this font that can be used freely. As of versions from 2018, the creator George Douros started to ask huge sums of money for obtaining a commercial license for using his ancient scripts fonts). Make sure to use the bold weight and not the regular one: the latter font is too light for usage in 'Brill' typeface context.