No, this is a common misconception about MySQL. In fact, the "length" has no effect on the size of an integer or the range of values it can store.

• TINYINT is always 8 bits and can store 2⁸ distinct values.
• SMALLINT is always 16 bits and can store 2¹⁶ distinct values.
• INT is always 32 bits and can store 2³² distinct values.
• BIGINT is always 64 bits and can store 2⁶⁴ distinct values.

There's also a MEDIUMINT, but the engineers who work on MySQL tell me MEDIUMINT always gets promoted to a 32-bit INT internally, so there's actually no benefit to using MEDIUMINT.

The length is only for display, and this only matters if you use the ZEROFILL option.

See an example in my answer to What is the difference (when being applied to my code) between INT(10) and INT(12)?