If you can use your old laptop as a recording device or if you can use it as a DAW with current up to date software are really two different questions.
I'm pretty sure you'll be able to use it as a recording device, if you don't do a lot of real time processing. Most of the work for recording will be done by the DCA chip of the audio interface anyway (be it in the motherboard or an external USB interface), the core of the PC itself will only do temporary buffering and writing of the recording file.
You may have problems with the DAW software if you use an update software version of an "heavyweight" application, as it may have difficulties running, both because of CPU and memory limitations. But an old software version contemporary with the laptop should run ok, or use a lighter software. Just for recording, Audacity is perfect and very, very light (I think Reaper is quite light too, but I've never used it with such an "old timer" PC).
If the operating system runs ok and with a light recording application, you don't need more memory to capture a couple of live tracks.
Now, a different story is using a DAW for editing and processing.
To manage and play a certain number of simultaneous tracks, the more tracks the more memory, so, depending on how the DAW manages memory, upgrading memory may help a little. But CPU will almost for sure be a severe limitation. When playing back, all the tracks need to be read from the audio files and processed and that uses a lot of CPU, specially if there are real time effects (EQ, compressing, etc.). The more plugins you use the more CPU you need. This gets worse if you use MIDI tracks with soft synths. It may help to render the effects and MIDI tracks to audio systematically, but that is too cumbersome to be used as a working horse DAW workstation (and BTW, how much disk space do you have to store all these audio files?).
In summary, you may be able to do some DAW work with your laptop, but choosing light applications and optimizing the environment is of the essence here. Get rid of anything that's not necessary for your audio work.
Upgrading memory may help (admitting you would be able to find appropriate memory DIMMs for such an old machine), but I wouldn't spend the money before actually trying it and see the results. You may find that CPU limitations alone don't allow you to do what you want.
Remember that when producers use old equipment, they are definitely not using the most updated version of the most powerful DAW in the market. They built an environment initially when they first got that machine and they have kept to it religiously for many years. I've read a report from a famous producer (I think it was Danger Mouse, but can't be sure) that even refused to connect is laptop to any kind of network, afraid that updates would ruin is environment.