Yes, I think that's quite questionable. British India seems not very relevant to the First Industrial Revolution in Britain (mid-late 1700s to mid-early 1800s).
Late 18th century Britain seems almost certainly due to industrialise. You've got substantial growth in per capita gdp (probably 250% India in 1700) and relatively high income consumers for goods (esp. nominally in world), a low share of employment in agriculture (something like 40% of population in 1700, low compared to most nations and comparable to Netherlands), productivity increases in every industry happening (huge growth in productivity for metals, fuel, construction, books; textiles like cotton actually not the essential or leading industry in output or productivity terms), and we know that science and technology are changing quickly purely on a qualitative level.
India looks much like a place that on a Malthusian decline through the 17th and 18th centuries, without much change under EIC. It doesn't have any of those features. It's not a place that's likely to industrialise its textile production, or anything much really. GDP/capita really only improves in the late 19th century a bit, with increased international trade, but even then that has limited scope by the Raj failing to make much impact in agricultural productivity or reduce share of population working in agriculture, and improve education (which is then a huge potential driver for growth).
Economic history may unfold quite differently throughout the 19th century (though I doubt much too "pulling a Meiji" as everything seems to indicate Japan was uniquely placed for that, but I wouldn't close the book on it with a good early divergence point), however the immediate story seems like it's not going to be vastly different in a world where there's empire in India.
In terms of talking about a weaker industrialisation, or at least weaker growth, the per capita growth rate seems fairly linear in Britain since about 1820 (indifferent in the medium term to changes and expansions in empire), so I'm a bit skeptical that it would be vastly different without British India (esp. given relatively low proportions of economy involved in trade etc) though of course the patterns of activity could change.