Absolutely not. It's a Code violation, because Code doesn't like having single points of failure where one ordinary and routine failure could burn your house down, or at least your generator (which would make a mess). And the failure in question is a common one we see all the time here. So no.
The issue is we can't have parallel/redundant paths for neutral. You must have only one path because if it fails we need the panel to fail. Otherwise neutral service current would siently take the alternate path, wildly overloading it.
And by the way, the problem isn't those inexpensive sliding-plate interlocks. We love those things and highly recommend them, as a rule.
But let's look at alternatives.
Consolidate all critical loads into 1 panel.
I gather this is a Class 320 aka 400A service, where they used two 200A main panels, and they're sitting right next to each other. If it's not I'll cover that next.
The savvy panel installer, whenever they put 2 service panels nearby, always runs at least 1 conduit between the panels, and preferably like 4. Why? Because you sometimes bring a circuit into panel 1 and then wish it was in panel 2. Under NEC rules, as long as the grounds are bonded, it's a simple matter of extending the hot and neutral wires through the conduit passage to the other panel. The circuit's safety ground can stay in the panel it was originally in, but the neutral MUST be extended to land in the same panel with the hots, Very Important.
For instance a friend had that setup. The right panel had only two 70A breakers for emergency heat (that the generator could never power anyway), and a 15A/120V breaker for the furnace air handler and thermostat. Moved that to the other panel and voilà, all critical loads are on one panel. Unfortunately sometimes builders "help you out" by scattering all your loads evenly across both panels. Well, that's what multiple conduits are for.
If the conduits are more than 2 feet long, you can have up to four 15/20A circuits in each conduit. If less than 2 feet long, look up the max number of wires allowed in that size conduit, you can have 150% of that many because of an exception. (e.g. if 14 wires allowed you get 21). Remember don't bring branch circuit grounds across. The best wire type to use for the extension wires is THHN, you must use white for neutral and non-white for hot. Tape the pairs (or triples) of wires together near each end so they are identified as the same circuit.
If the panels are right next to each other and even with each other, I would find two knockouts that are directly across from each other, get an "RMC conduit nipple" (aka short pipe) 1/2" to 1" longer than the gap, and 2 conduit nuts. That won't do for grounding, but it'll work as a pass-thru. If there is lumber in the way, consider powering down one panel and doing some "dental work" with a Dremel moto-tool to remove the offending wood.
Now that all your critical loads are in 1 panel, you know what to do!
Or, isolate with a transformer
Another way to create the essential neutral isolation, and still use the inexpensive interlocks, is to watch Craigslist for a domestically made, UL Listed 120/240V--240/480V isolating supply transformer. I occasionally see them pop up for $100-200.
You only need the transformer on one of the two panels. The goal is to disconnect neutral between them. So do it on the smaller panel.
Jumper the transformer primary (480V side) for 240V (parallel both windings) and that goes straight to the generator inlet.
Jumper the transformer secondary (120V side) for 120/240V. Neutral goes straight to the neutral bar. The two hot wires go to your generator interlock breaker, which is sized to protect the transformer from overheat. Take the "KVA" of the transformer (e.g. 5 KVA) and multiply by 4 to get amps (20 amps).
Transformers are sized 5, 7.5, 10, 15 KVA. If the transformer isn't sized like that, you're looking at the wrong kind of transformer. If they come in a black or red box with a goofy "everything socket" on the front, that's definitely the wrong kind, that's not even an isolating transformer and its' cheap junk off Amazon. Don't do that.
Or, a 3-pole "big knife switch" transfer switch on one panel
This is the other way I can offer. This will be wired to switch neutral (as well as the two hots) from utility to generator. Again, you only need this on one panel.
Unfortunately it must be sized for the largest current (i.e. 200A utility current) so it will be a very costly switch. Seems unlikely to be affordable, so I won't discuss it further.
Note that those hokey and costly 6/8/10 circuit "transfer switches" are of absolutely no use here. They do nothing to solve the problem at hand, they just waste money.