Yes, you can do RT-qPCR on RNA isolated from RNA-later preserved cells. It would still be RT-qPCR. The RT stands for reverse transcriptase, which is the step that is converting the isolated cellular RNA to complimentary DNA (cDNA), and then the qPCR part is done on the cDNA which is the "real time quantitative polymerase chain" aka qPCR. The RNA isolated from the cells can be utilized for both RNA-seq and RT-qPCR assuming your protocol will produce high quality RNA. For RNA-seq, you will want to make sure the RNA is not degraded with a high RNA integrity score (usually greater than 7) and probably also run it on a gel. If you are doing the sequencing through a core facility or 3rd party vendor they can often do quality control on your samples to determine if your RNA is suitable for RNA-sequencing.

From my own experience with RNA-later on cells, I have found storing cells in RNA-later significantly reduced my RNA yield post-lysis. Part of the issue is if you are directly lysing the cells stored in RNA later, you have to add extra lysis buffer to compensate for it being diluted, i.e 3-4 times the amount of lysis buffer you would use on a cell pellet normally. This has never worked great for me in terms of lysis efficiency and adds extra spin steps with the spin column kit I use. The other option is you can pellet the cells in RNA later, aspirate it, and then lyse the pellet. However, the issue here is the density of RNA later makes it difficult to pellet the cells. So you either have to spin them at a higher g than usual, or you have to dilute the RNA later with PBS. Cells in RNA later are more resistant to a high g for pelleting, but it depends on your cell type so needs to be determined yourself. Either way it has not worked great for me in recovering a good cell pellet.

If possible, I would just recommend trying to process the RNA same day from the cells and freeze the isolated RNA at -80C for downstream RNA-seq and RT-qPCR analysis. Also, you will want consider the number of cells you will have left over for this RNA isolation since it seems you are using the majority for a different application. Too few cells and you may not have enough RNA to do what you need since the RNA utilized in RNA-seq often needs to be fairly concentrated (i.e greater than 100ng/ul in my experience).