先不说句子转换问题，我认为这个句子本身有误。错误在于句子主语Many boys，用词不当，逻辑讲不通。改为 Many men或Many adult men，所以，句子应为：

Many men, having had few advantages in their youth, have nevertheless done great things for their country. 

【翻译】许多成年男子虽然在青年时期没有什么优势，但却为国家做出了巨大的贡献。

【分析】having had few advantages in their youth, 是个非限制性定语，表示“让步关系”。

1. 如果转换为从句，句子时态应为一般过去时：

Many men, who had few advantages in their youth, have nevertheless done great things for their country. 

2. 转换为两个独立的单句也可：

Many men had few advantages in their youth. They have nevertheless done great things for their country. 

关于句子的时态问题，前面两个老师已有了很好的分析。我这里想说说网友这个句子的正确性问题。

Many boys, having had few advantages in their youth, have nevertheless done great things for their country.

我觉得这里的many boys与后面的 in their youth 并不矛盾。因为 boy 不仅可表示男孩，而且也可以表示“男青年”（a male child or a young male person）。对于一个“青年人”来说，他/她至少经历了三个“时期”：babyhood（婴儿期）、childhood（儿童期）、youth（青年时期）。网友的句子指的是：许多青年人在其青年时间（而不是婴儿时期或儿童时期）没什么有利条件，但仍为自己的国家做出了伟大的贡献。

上面这个句子出现在章振邦教授的语法书里，而且不像是排版错误，所以其正确性应该是可以肯定的；我在印象中在北大董桂枝教授编著的《英语特殊表现法例解》也见过类似的句子，为确实起见，我特在这本书时找到了这个句子：

Many girls who have had few advantages in their youth have done great things for their country. 许多女孩子虽然在她们青年时期没啥有利条件，但仍为他们的国家做出了伟大的事业。（《英语特殊表现法例解》第132页）