In theory yes. The idea is that committed buyers (upward breakout) or committed sellers (downward breakout) will cause volume to increase because they are keen to buy or sell and move the price to get their business done.
Most of the textbooks are from the US and they stress that a breakout should have an increase in volume to be reliable. Three comments:
1. I am always distrustful of "textbook examples". Too often someone has a theory and finds an example to prove it.
2. Most of the US examples seem to come from the major stocks. It is probably valid for them. I wonder about smaller stocks. In Australia, we have lots of smaller stocks.
3. An increase in volume on a breakout makes us feel warm inside and more comfortable, because we have read the theory. However, from long experience, I have seen too many good breakouts with low volume, especially on stocks outside the top 100.
Personally, I don't worry about volume any more on breakouts. Price is 90+% of the picture. Volume is nice, but only a confirmation and worth far less consideration than price.