I'm an avid manga reader and my absolute favorite manga of all time, Takane and Hana, just revealed that it is getting a live action drama. I don't exactly have the best opinion on J-dramas (I find them unbearably goofy), and I know that the premise and story will be extremely hard to make work with real life people. I've always hoped that Takane and Hana would get an anime, but now that it has a drama I don't know if it can. If anyone knows anything that might help I would greatly appreciate it!
Whether Takane & Hana will ever receive an anime adaptation is off-topic for this site, since that concerns unannounced future events. However, I will try to address the broader question of whether manga ever get anime adaptations after receiving live-action adaptations.
Off the top of my head, there is some precedent for live-action adaptations, whether television dramas or films, being created prior to anime adaptations. For example:
The Nana manga ran from 2000 to 2009. The film adaptation first came out in 2005; the anime was released in 2006.
The Perfect Insider originated as a novel in 1996. A manga adaptation came out in 2001 and a game in 2002, and a television series was broadcast in 2014. An anime adaptation was released in 2015. Note, however, that the television series contains material without the original novel that the anime did not adapt.
The Great Teacher Onizuka manga first ran from 1997 to 2002. A television drama came out in 1998, and an anime series in 1999.
Yamada-kun and the Seven Witches ran from 2012 to 2017 as a manga. The television adaptation was broadcast in 2013, the anime in 2015.
Superficially, the answer then is yes, manga sometimes get anime adaptations after receiving a live-action adaptation. However, many of the dates in my examples are relatively close, and without doing much more research, it is unclear to me when the announcements and decisions about the adaptations were made. It is possible that a television series and an anime released only six months apart might have begun production or been announced at around the same time.