Hi,
You did say planer thicknesser so yes, you can straighten boards with it in planer mode. There are cheaper thicknesser only machines that have their uses, but are much less versatile. You can of course straighten with a decent hand plane!
A lot depends on your budget as you really do get what you pay for. I have what some might consider a budget machine but it works well for me. It is a Scheppach HMS260 (the earlier model with fabricated not cast beds) that I bought ten years ago and it was one of my best ever tool buys. It has several particular advantages over similar machines; rubber feed rolls instead of serrated wheels, can machine down to 3mm thick, has a powerful motor and it can be used without a chip extractor without clogging. Of course a chip extractor is preferable, but like I did, buy it later.
I use mine for a variety of work from planing oak boards for furniture making to planing spruce for my homebuilt aircraft project. It is fitted with a Wixey digital thickness gauge which has turned it into a precision tool and I find myself able to work to really close tolerances with it.
The only downside is that it takes/wastes time changing from one mode to the other but I don't really have space for a dedicated planer/jointer too.
If you buy one, do find a local experienced woodworker to help you get it set up accurately as none leave the factory as well set up as they can be. Also get some instruction on how to use it efficiently and safety as those blades can evaporate fingers! Woodworkers tend to a friendly lot.
Do buy one, having it and a decent band or table saw will transform your scope of work.
Regards,
Colin