Good question "Can I charge those batteries faster by starting the in house generator at the same time charging from two sources?"
"GENERALLY SPEAKING" YES its like filling a swimming pool with two garden hoses versus only one HOWEVER this is all subject to the quality and capacity of your in house charger/converter as well as how your alternator is set up to charge the house batteries when driving.
If you use wire to basically place the house battery in parallel with the engine battery when driving, how many actual charging amps the house battery may get is subject to the wire size, length of the wire run, and the alternators regulation. In addition be sure to NOT overload the engine alternator. Often (subject to many variables) the quality of this charging scheme doesn't yield a high degree of quality or quantity house battery charging, but hey if it pumps any charging amps it can help. It will NOT be the same quality and completeness of charge a 3/4 State Smart Charger would provide. NOTE its best if the house and engine batteries are the same chemistry in this situation. While Ive used this method over the years and sure it can "help" it never seems to fully or completely charge the house batteries like my onboard 3/4 Stage Smart Charger can.
For a better system use a DC to DC Charger that shouldn't over tax your alternator plus provide a better quality charge to the house battery when driving.
John T BSEE,JD Retired Electrical Engineer and 49 year RV owner