No, these Methor, Muchi, Dom of Dravidian stock of soth India were brought in by the British govt. British also took many thousdands of Tamils to Sri Lanka for rubber plantation work. They also sent many of the south Indian Dravirs to Malay, also to work as labours in the rubber plantation.
Although these Methor Dravidians were brought in by the British, but Bangalis also have a little mix of Dravirs in their blood since the very ancient times. Rakhal Das Bannerjy was one of the most prominent Historians during the British time. He was active in the discovery of Mohenjodaro and Harappa civilization, now in Pakistan.
'Bangalar Itihash' is a history book composed by him. He wrote in that book something like this, 'Uttor Theke Elo Mongol, Dokkhin Theke Elo Dravir, Aar Choto Nagpur Theke Elo Negro Jatio Jonogosthi. Ei Tin Jater Shongmisrone Sristi Holo Adi Bangali. Tara ki Juddhobigroher Madhyome, Na Ki Eki Mondire Eki Bigroher Pujo Dewar Madhyome Porshpor Poroshporer Majhe Bilin Hoye Gelo Ei Tothyo Itihash Deyna'.
There are some tribes such as Shaotal who probably remain without any further mixing of people who arrived in this land in latter times, during both Hindu and Muslim period. But, most of the 1st assimilated people were further assimilated during many Centuries of pre-Islamic time when many other groups also migrated from all the area that surround Bengal.
Muslims from the central asia and poor Arab countries were the new addition to the migration process. These people were again assimilated into those locals who took Islam as their religion. This is an ongoing process. But, initially, there were very few mixing of bloods between those foreign Muslims whose status was above the local converts.
In the course of many centuries, the mixing is still not complete. However, it will continue.