The basic invention process does not take on any researched attributes of the BPOs or BPCs.
The only attribute of the BPC that affects the BPC output in the invention process is the number of runs on the copy. Generally you will either always want to use 1-run copies (mostly when inventing ships) or max-run copies (mostly when inventing modules or ammo). This comes into play when you use decryptors (or choose not to use one). These affect the invented Material Level, Productivity Level (Manufacture Time), Runs of the invented BPC, and invention chance.
However, there is still an indirect effect of ML/PL on BPOs. Usually when you make a T2 item, you have a few input products that need to be made which are consumed to make the T2, such as a T1 version of the item, and Construction Components such as Tungsten Carbide Armor Plates or EM Pulse Generator. Material levels on these BPOs mean you'll usually need to use less Moon Materials or other materials, which could lower your final cost of making the T2 item.
Putting all of these options together to figure out which is the best option to maximise profit is the interesting part of T2 manufacturing.