I think the idea is good, but I don't think it works in reality very well.
Joining the EU was supposed to benefit poorer countries like Romania and Bulgaria by enabling them to attract inward investment into their countries. IE if a big company wanted to build a factory they would be encouraged by Brussels to go Bulgaria, they would have the same guarantees as if they were setting up in Germany, but with a much cheaper workforce. A huge amount of money was paid in grants to move factories and other production facilities from this country to East Europe, Cadbury's was one business that did this.
What has happened is that these countries are losing too many of their most talented and enterprising workforce, who are all coming west for better wages. Bulgaria loses something like 80% of its newly trained doctors as soon as they qualify. It is affecting their ability grow their own economy and is just not sustainable long term.
Many of the Eastern European workers who come here work in appalling conditions, and are being really badly exploited. A friend of mine has been working with people who have been treated as virtual slaves, it is horrible to think of it happening in a so called civilised country - and no one really cares.
There are many other similar stories which make me say that no, in practice it does not work very well at all.