Can I process RGB, VNIR, or SWIR data if I do not have LiDAR data/Point Cloud or DSM captured at the same time?

Yes, RGB and VNIR data can be processed without LiDAR data from the same flight in different ways, each with varying implications on orthorectification quality:

1. For both RGB and VNIR, you can use a DSM from a different date (as close in date as possible to the flight you want to process). Edit or create a pipeline with an RGB or VNIR task. For your mosaic product, under Digital Surface Model, select Select Other and browse for a DSM from a different date of that site. 
2. Publicly available DSMs, from sources such as USGS, may also be used. See the FAQ "Processing with USGS DEMs" above. 
3. An additional method is to use an RGB generated sparse point cloud. To create a Sparse Point Cloud, edit or create a pipeline with an RGB task. For your mosaic product, under Digital Surface Model, select Sparse Point Cloud. VNIR and RGB DSM options will allow you to select the newly defined RGB sparse point cloud. 
4. Hyperspectral and RGB tasks have the option to use a fixed elevation value. If the survey area is relatively flat, a fixed value above ellipsoid can be set in the processing configuration in place of a DSM or point cloud. The value should match the nominal height of the scene in the same reference frame as the GNSS-INS export trajectory (WGS84 height above ellipsoid by default).